Melt butter in large pot over medium. Cook onion, carrots, and mushrooms 8 to 10 minutes until loose mushroom water cooks off.
Stir in wild rice and sherry 1 minute. Add broth, thyme, salt, and pepper; simmer.
Partly cover; gently simmer 25 minutes without hard boiling.
Add chicken; simmer 20 to 25 minutes more until chicken 165°F and rice tender with some grains split. Cook rice another 5 minutes if centers remain hard.
Rest off heat 5 minutes; stir and divide rice, chicken, and broth evenly among bowls.