Required Preperation
Whilst the chess event is the least challenging fight by the time you are this deep into Karazhan, there are a few precautions to take before you engage this fight to make it go smoothly.

Ensure that people know which units to control first. Initially you'll need a few people controlling the front row units just to allow the rear ones to pass.

The Game

As you can see from the screenshot, the pieces are divided into two teams. On the left an Alliance team, and on the right the Horde. The abilities and pieces available to each side are in essence the same, different only in looks and name. If you are Alliance, you will control the Alliance side, and similarly Horde raids will control the Horde side.

The game is initiated by talking to the king of your relevant side when you are ready to begin, and it should be ensured all members are ready to play before anyone does this.

Before the fight is initialised, only the king piece of your side will talk to you. Once the fight is started by controlling the king, you may talk to any other unit to request control of it. They won't talk to you, however, if you have a 'recently controlled' debuff.

Understanding The Controls

This screenshot shows the old style pet bar controls for the pieces. The encounter has since updated so that there is no need for a pet bar, but this image still shows the piece abilities.

1+2+3) These are standard pet controls but serve no purpose in this fight and can be ignored. Pieces will automatically melee any unit directly in front of them.

4) Move : This unit tells the piece to move. Click this button then target the square on the board with the reticle that comes up. Each unit may move a certain number of spaces before waiting 5 seconds to move again. Refer to the Unit Breakdown section below for more details.

5) Rotate Piece : As mentioned before, pieces will automatically melee any unit directly in front of them. This function is useful for turning the piece to attack a unit to the side of them or to turn and use special abilities with a frontal component. Click this button then click the adjacent square you would like to turn and attack.

6) Special ability 1 : This is the ability shown at the top of the above screenshot but is specific only to this unit and will be different for non-king pieces. As the tooltip in the picture states, it will hit all 3 hostile units in front of the king. In the below picture the three squares affected by this ability are covered by the red bar.

7) Special ability 2 : Refer to unit tables below

8+9+10) These are more standard pet controls and set the stance of the unit. They can be ignored during this encounter.

Unit Breakdown
First, lets get a breakdown of the pieces on each side.

Piece 1: Orc Grunt/Human Footman - Low health/Low damage/Weak Specials
Movement: Any adjacent single square.
Special 1: 1000 damage to unit directly in front of piece.
Special 2: 500 Physical damage absorbed for 5 seconds on self.
Notes : Use only special 1 as the damage absorption is paltry compared to the damage units on the board do. This unit is low value and is well used to distract other units.
Value : 6th - This is the lowest value unit and as such is expendable.

Piece 2: Summoned Demon/Water Elemental - Low Health/Medium Damage/Strong Specials
Movement: Any adjacent single square.
Special 1: 3000 damage to any adjacent unit.
Special 2: 50% damage reduction for 5 seconds on self.
Notes: Use special 1 whenever any unit is on any of the 8 adjacent squares to you, the more units you can hit the more efficient this unit is. Low hp and slow movement are the downside to this unit but with enough enemies nearby it can also be quite potent!
Value : 4th - High damage but low health makes this situational but useful.

Piece 3: Orc Wolf/Human Charger - Medium Health/Low Damage/Situational Specials
Movement: 2 squares in any direction or 2 squares in 1 direction + 1 to the side.
Special 1: 3000 damage to the unit directly in front.
Special 2: -50% damage to all adjacent units for 10 secs.
Notes : While offensively quite weak the speed of this unit can be utilised to keep high damage enemies supressed.
Value : 5th - Whilst this unit has utility its low damage makes it fairly expendable.

Piece 4: Orc Necrolite/Human Cleric - Low Health/Low Damage/Support Specials
Movement: Any adjacent single square.
Special 1: Heal any targetted unit for 6000.
Special 1 Range : around 1/2 the board's length.
Special 2: Hit all units within the 3 squares in front of the unit for 2000. The target of this attack is 3 in a straight line not the adjacent 3.
Notes: The heal is very potent on these and can be used to turn the tide of the battle! Use wisely and concentrate mostly on your king. Special 2 is also nice for dealing damage from range without putting yourself at risk.
Value : 3rd - The sheer usefulness of the healer makes this a valuable unit.

Piece 5: Orc Warlock/Human Conjurer - Medium Health/High damage/Strong Specials
Movement: Straight - 3 or Diagonal - 2.
Special 1: 4000 damage on targeted enemy.
Special 1 range : Straight - 4 or Diagonal - 3.
Special 2: 6000 damage on target + all adjacent units.
Special 2 range : straight - 4 or Diagonal - 3.
Notes : The single target abilty has a low cooldown on this unit and can be used to take a target down quickly. While the AoE has a longer cooldown, it's devastating on a group of enemies when targeted on the centre unit. High movement speed and very high damage makes this the most dangerous unit on the board.
Value : 2nd - Very good damage, high movement value. Keep this one alive.

Piece 6: Warchief Blackhand/King Llane - High Health/High Damage/Powerful + Utility Specials
Movement: Any adjacent single square.
Special 1: Hit the 3 units adjacently in front of the unit for 4000.
Special 2: All adjacent friendlies gain 50% damage for 10s. This ability does not affect the king piece itself.
Notes: This guy must be kept alive at all costs. His slow speed means he can be chased quite easily however he has very high health. His attacks are quite potent and special 2 utilised near a bunch of friendlies can help take the enemy team down much quicker.
Value : 1st - Without this unit the game is over, keep alive at all costs.

Special Ability Cooldowns
When an ability is used it triggers a cooldown on the other ability equal to its own cooldown but not exeeding the highest cooldown of the other ability. What this means is if you have 5 and 15 second cooldown abilities and use the 5s, the 15s one will be on a 5s cooldown. Alternatively using the 15s one would put the other ability on a 5s cooldown.

Piece 1 ability 1: 5s
Piece 1 ability 2: 5s

Piece 2 ability 1: 5s
Piece 2 ability 2: 5s

Piece 3 ability 1: 5s
Piece 3 ability 2: 5s

Piece 4 ability 1: 10s
Piece 4 ability 2: 5s

Piece 5 ability 1: 5s
Piece 5 ability 2: 15s

Piece 6 ability 1: 5s
Piece 6 ability 2: 15s

The Fight
So long as you have an understanding of what each unit does from the previous section it's fairly simple to actually win the fight. While the AI team reacts differently every fight, the overall strategy remains the same.

In order to release control of a piece right click the buff on your buff list called 'Controlling piece'. You will get a debuff lasting 20 seconds preventing you from controlling a new piece until it wears off.

Stage 1: Get some team members to control the 4 middle units on the front row and move them forward either 1 or 2 squares. This opens up space to the units behind whilst leaving space to retreat later. Get the remaining people to control at least the leaders, warlock/conjurer and healers.

Stage 2: Concentrate on the enemy healers. The healers have low health and a concentrated charge on each one in turn should cause them to drop rather fast. Assuming you've cleared space, your team's offensive units (Wolves/Chargers,.Elementals/Demons or any grunts) should move forward swiftly. The Warlock/Conjurer should move forward and nuke the enemy healers with either special whilst maintaining a safe range. Using the Wolves/Chargers during this time is a good way to supress the large crowds of enemies. Move the king forward to utilize his damage buff but do not send him deep into enemy lines. Your Necrolites/Clerics should remain near the back and heal any damaged units, focussing on the special units before the grunts/footmen.

Stage 3: Once the healers are down, the main focus is the enemy king. All other units should be ignored. Without healers he will go down fast. Bring all units close enough to use their special abilities, priority being given to non grunts/footmen. Keep your leader slightly back and use his buff with the healers further behind him. With their leader trapped and no-one to heal him he will go down very fast.

As long as the fight is taken in the stages mentioned above this fight won't last long and will be rather simple. Dont be afraid if you lose a unit so long as something good comes of it. Keep your king and healers healthy and you should be fine.

Once the opposing king is dead the chest with loot in will spawn next to Medivh's shade