On Thai menus this is called Tom Kha Gai. It's always yummie, even when the restaurant doesn't get it quite right.
I found the recipe I used on the Food Network website. Most of you know I live out in the middle of nowhere, so there was no way I was going to be able to find galangal, or kefir lime leaves at my local grocery store. But I did find something called Gourmet Garden Thai Herb & Spice Blend. It's kind of like a paste. It has lemon grass, ginger, cilantro, garlic and chili peppers. So, in the recipe, when it calls for these ingredients, I used the paste. I substituted strips of lime zest for kefir lime leaves.
Here's a link to the recipe on Food Network's site.
I have to say, I think the soup turned out really well. Next time I'll use more coconut milk, though. It just wasn't quite creamy enough for me.
Of course, next time I make it, I'll use the Thai food kit I ordered off the internet yesterday! :) I'll make it again with the real ingredients, and tell you how it compared to this...