Melt butter in a large pot and cook onion, carrots and mushrooms over medium heat for 8 to 10 minutes until the mushrooms lose their loose water.
Stir in wild rice and sherry for 1 minute. Add broth, thyme, salt and pepper and bring to a simmer.
Cover partly and simmer for 25 minutes, keeping a gentle bubble rather than a hard boil.
Add chicken and simmer for 20 to 25 minutes more until the meat reaches 165°F and the rice grains are tender with some split open. Give the rice another 5 minutes if its centers are still hard.
Let stand off the heat for 5 minutes, then stir and divide the rice, chicken and broth evenly among bowls.