In a sauté pan large enough to hold the chicken in a single layer, heat the olive oil over medium high heat. Season the chicken pieces with salt and pepper. Add chicken to pan, skin side down and sauté for about 4-5 minutes per side or until chicken is browned.
Remove chicken from pan and reserve. In same pan, add butter. Allow the butter to melt over medium heat. Add squash and sprouts to pan and sauté, tossing occasionally, until the outsides are golden brown, about 3-4 minutes. Remove from pan and hold separately from chicken.
Turn heat to high and add stock, syrup and mustard. Stir and bring to a boil, stirring to scrape up the brown bits on the bottom of the pan. Add chicken back to the pan, cover, and reduce heat to medium low. Cook over medium low heat for 20-25 minutes or until chicken registers 170 degrees F with an instant read thermometer.
Add vegetables back to pan, cover again, and cook for another 8-10 minutes until the vegetables are tender. Remove chicken and vegetables to a serving platter, placing vegetables around chicken. Turn heat to high and boil sauce until it is reduced and slightly thickened, about 2-3 minutes.
Spoon sauce over chicken and serve.