Mix apricot preserves, Russian dressing, soy sauce, yellow mustard, onion, and garlic together in a large bowl.
Place chicken pieces into the apricot mixture and stir to coat.
Transfer chicken and sauce to a baking dish.
Bake in the preheated oven until the sauce is bubbling and thickened and the chicken is no longer pink inside, 45 minutes to 1 hour. Turn the chicken pieces twice while baking.
If sauce seems thin, transfer chicken to a platter; place baking dish of sauce under broiler until sauce has thickened, 2 to 5 minutes.
