Tips: the lemon grass, lime leaves and kha are best left in large pieces to make them easier to pick out later, as they are tough and inedible. I leave them in all the way till serving and tell my guests to look for them and set them aside as they eat. The RecipeZaar ingredient format makes it hard to enter how much galangal (kha) to use: I use a root-knob about twice the size of the ball of my thumb. I use half of a 4-ounce tin of red curry paste (4 tablespoons) for a pretty spicy-hot soup; you can use 1/4 can for milder heat, but the recipe for Tom Kha Gai on the Maesri tin calls for the whole thing- WOW that must be hot!
In a large stock pot, saute the curry paste, garlic, lemon grass, lime leaves and kha in the vegetable oil for two minutes.
Stir in chicken broth and bring to a boil.
While broth is heating, slice the chicken breast and toss it in cornstarch. The amount of cornstarch doesn't need to be exact; just make sure the slices are evenly coated and shake off any excess.
Add chicken to boiling broth, stir gently, and bring back up to a simmer.
Stir in mushrooms, coconut milk, fish sauce and lime juice. Bring back up to a simmer, stirring gently a few times, then cut the heat off and you're ready to serve.