After completing a number of jobs in Solitude (5 or so, I think…), Delvin will have this "Special Job" for you. It seems our actions have brought the guild some attention! We are to travel to Solitude and speak to a merchant named Erikur. You can find him hanging out in the Blue Palace during the day.
Erikur is after what most people are after: revenge. He’s been cheated by a captain named Volf of the Dainty Sload, and now wants you to acquire something called Balmora Blue and stash it aboard the Dianty Sload in Volf’s footlocker to frame him. Head to the docks to find a woman named Sabine who ferries contraband to and from Morrowind. She will sell you some Balmora Blue for the HIGH, HIGH price of 1,500 Gold! You can ask her if there is another way to earn it, but she wants cash so pay up (you can come back later if you don’t have the cash now). When you pay up, she’ll give you the key and advise that the chest is under the dock nearby, so jump into the water, unlock the chest and grab the Balmora Blue.
We’ll now have to plant it on the Dainty Sload. Easier typed than done. We will need to be EXTREMELY SNEAKY here (or you could use magic to your advantage, or maybe even an invisibility potion or two as insurance. The Dainty Sload is full of corsairs that will attack you on sight. Wait until night and sneak aboard, as the only entrance is the door on the deck. A pirate will be out here but won’t attack as long as you back off, so wait until he is busy before entering.
Once you’ve entered, loot the chest to the right. Down the stairs are two pirates that are talking in a room to the left, letting you sneak by them. Past that is a door with another pirate hanging around the next corner. THIS pirate switches between sleeping and sitting on the bench, so wait until she sleeps to get by. You’ll be down in the storage area now where a single pirate patrols. There is a chest to the right by the stairs that lead down here. It can be HARD to get by this pirate, but they will occasionally stare off to the north which will let you get by.
You are now in the Captain’s area. The first mate is around here but SHOULD be asleep. If not, wait until he is. The reason we want him asleep is because on the desk where he usually sits lies a Stone of Barenziah as well as a SPEECH SKILLBOOK named "A Dance in Fire, v6". Now you can either pick the Captain’s Footlocker or pickpocket the key off of the first mate and open it. Take out everything inside and leave the Balmora Blue. Now we have to make our way out of the boat the same way we came in (if all else fails, run!).
Make your way back to Erikur and let him know that you’re done. He already knows, but will give you the Calm spell tome as thanks. Make your way back to Delvin and let him know you are done as well. Congratulations! Now go do more Thieves Guild missions!