Take the chicken out of the pan and pour off all but 2 tablespoons of the drippings.
Return the chicken to the pan, add the coconut milk and beer, and bring to a boil.
Reduce heat, cover the pan and simmer until the chicken is almost tender, about 30 minutes.
Add the vegetables and season to taste with salt and pepper.
Simmer, uncovered, until the liquid has thickened to the consistency of gravy, about 15-20 minutes more.
If the liquid evaporates before then, add more beer.
NOTE: I used boneless skinless chicken breasts and a 12-ounce bottle of Shiner Bock when I made this, and it turned out great.
NOTE: You can also use cream of coconut instead of coconut milk (I did this by accident the first time I made it, not realizing that there was a difference!)- it still comes out tasting good, but the resulting dish is a lot sweeter than if it's made with coconut milk.