Put the stock, ginger, lemon grass, and lime leaves or lime peel in a stock pot. Gradually bring to boil over medium-high heat. Boil for one minute, then add the coconut milk. Return to boil, then add the chicken. Return to boil, and then add the chili-tamarind paste, the lemon juice, sugar, and fish sauce. Stir until the paste and sugar are dissolved and blended, then add the mushrooms. Simmer until mushrooms are tender, about 1 minute.
Float chilies on top and turn off the heat. Serve.
This is from one of my favorite cookbooks, True Thai by Victor Sodsook. I've now made it twice, and it turned out delicious both times. This dish is among both my favorite Thai foods and my favorite soups.
I used the lime peel option, the galanga, and palm sugar. The only place I've managed to find galanga is Uwajimaya. Both times I've been a bit heavy on the chicken, just because that's what the package was.
I've deviated from and modified the above recipe in the following ways.
Instead of chili-tamarind paste (which I couldn't find, and didn't feel like making), I used a mix of sweet chili sauce and tamarind extract. While this seems to work well for flavor, I'm thinking about adding something to make the dish hotter.
Since I used stock from bullion both times, I made up the stock first, and added the galanga, lemon grass, and lime peel to that pan, and then let it sit while I prepped the other ingredients.
Similarly, I prepped the sugar, juice, fish sauce, chili sauce, and tamarind extract into a bowl ahead of time, though I'm not sure that actually saved me any effort.
The second time I made it, I used the juice from the lime instead of lemon juice, and it worked fine.
The Siamese ginger, lemon grass, and lime peel/leaves aren't meant to be eaten. Eating the chilies is an option for the hardy.