Thieves Guild: The Elven Maiden
After you have fenced at least 100 golds worth of stuff, you'll get a journal entry telling you that Armad Christophe may have another mission for you. He does.
The mission is simple enough: steal the bust of Llathasa Indarys, the late Countess of Cheydinhal. Fast-travel to Cheydinhal and bribe up one of the beggars to learn that the bust is in the Undercroft of the Chapel of Arkay, which is guarded and reportedly haunted. Ha! Guards and spooks? And you thought Armand was going to ask you to do something difficult. So off to the Chapel you go. As you are looking up the stairs, use the left-hand door since it will speed your getaway. You'll need to pick the lock to get in, but you did bring a supply of lockpicks, right?
The guard patrols a set route and the spooks aren't even there when you enter. The bust is going to be in a small chamber to your left (which is why we're using the left-hand door). So drop into Stealth mode, wait for the guard to leave on a patrol circuit, and then nip in, grab the bust and nip back out again. Easy-peasy. If you're slow about it and the guard returns, just find a dark corner, sit still and wait for the next patrol. The spook won't even appear unless you try to open the sarcophagus. Don't get greedy or click on the wrong thing and you'll be fine. When you're out of the Chapel, fast-travel back to the Waterfront to report your success to Christophe.
Only one problem. The Waterfront is crawling with guards, including Hieronymus Lex, and all of them are looking for Armand Christophe, who is nowhere to be found. Actually he can be found, but you'd have to know exactly where to look to find him. He's in the basement of the Imperial Trading Company warehouse at the far end of the district. But he won't tell you anything other than to find Methredhel to get your instructions. Your fellow thieves aren't much help beyond letting you know that Methredhel is looking for you. You'll find her pretty quickly and get some new instructions. It seems that the guild has been infiltrated, ratted out, exposed... you get the idea. Anyway, Christophe is in hiding until the mess can be straightened out. And you are the lucky one who's going to have to do the straightening.
The infiltrator is Myvrynra Arano (remember, the one person in the district who didn't have to pay taxes?). You can get this information from Hieronymus Lex if you happen to be standing nearby when he drops that little tidbit in a conversation with a guard. Otherwise, Methredhel will tell you when she finds you. No matter how you get that information, you'll need to pin the theft on Arano. Arano has a house in the Waterfront District, just to the south of where Lex is standing. When no guards are looking, pick the lock on the door, sneak over to the cupboard in front of you and activate it to deposit the bust. OK, now that the evidence is planted, you need to let Lex know about it.
Unless you have an exceptionally high Personality or have dealt with him before, you're going to have to get his Disposition up to 70 or better. Surprisingly enough, bribery works quite well and he loves it when you intimidate him - go figure. Failing that, Disposition-boosting spells will do the trick, too. If you've been progressing in the Mage's Guild, too, you might even have a couple of suitable scrolls left over from Kud-Ei's recommendation quest. Anyway, the Disposition boost doesn't have to be permanent. It just has to last long enough to start the appropriate conversation thread. Talk to him about the bust and tell him that the bust is in Arano's cupboard. He doesn't really believe you, but decides to investigate and insists that you follow him while he he does it.
You get to listen in on his conversation with Arano (whose cover is now blown) and watch her get carted off to jail (watch her face as she leaves; if looks could maim, you'd be a basket case). The crisis has passed, the Guild has been saved and Christophe will return to his appointed place in the Garden of Dareloth at the next midnight.
The next time you talk to him, you collect your 100 golds, get promoted to Bandit, get a new fence (Dar Jee in Leyawiin), and get shuffled of to S'krivva in Bravil for your next mission. Unless you need to use him to pay off bounties, you won't be seeing Christophe again until after you complete the entire Thieves Guild questline. Well, Armand, it's been real and it's been fun. "May Shadow hide you" and all that.