Yes! If you don't have access to an outdoor grill, you can easily oven grill the chicken by using the broiler in your oven. Drumsticks and thighs take about 40 to 50 minutes to oven grill. Breasts take around 25-30 minutes. You can also oven bake the chicken in the oven on 350°F for 30 minutes or until the internal temperature reaches 165°F in the thickest part of the meat.