In a small bowl, whisk together the mayonnaise, Italian dressing, garlic powder, and red pepper.
MARINATE THE CHICKEN
Place the chicken in a dish or in a large Ziploc bag. Pour the marinade over top. Toss to coat the chicken with the marinade. Cover and refrigerate for at least 20 minutes (or up to 24 hours). Remove chicken from the dish. Discard marinade. Allow chicken to sit on the counter at room temp while you prepare the grill or preheat the oven.
TO GRILL THE CHICKEN
Heat a nonstick pan, grill pan, or outdoor grill over medium-high heat. Coat the grill grates or pan with about a teaspoon of oil so that the chicken doesn’t stick. Sear or grill the chicken on each side until golden, crispy, and cooked through (about 5 minutes per side for small, thin chicken breasts, up to 10-12 minutes per side for larger, thick chicken breasts, or about 6-7 minutes per side for chicken thighs). The meat is done when it reaches an internal temperature of 165°F. Allow the chicken to rest for about 5 minutes before slicing and serving.
TO BAKE THE CHICKEN (ALTERNATE INSTRUCTIONS)
Line a large, rimmed baking sheet with foil and lightly coat with nonstick cooking spray or lightly grease a 9 x 13-inch baking dish. Remove the chicken from the marinade (discard the marinade). Bake the chicken in a 425°F oven for 20-30 minutes for thin, small chicken breasts, about 30-45 minutes for thick, large chicken breasts, or about 20 minutes for boneless, skinless chicken thighs.