Add the chicken breasts to a shallow baking dish for marinating.
In a small mixing bowl, whisk together the cayenne pepper, brown sugar, chili powder, paprika, garlic powder, olive oil, and vinegar. Pour this marinade over the chicken in the baking dish. Let marinate for at least 2 hours before cooking - slow cooking, pressure cooking, or grilling. All 3 cooking directions are below.
SLOW COOKING: Place the chicken and marinade in the slow cooker and cook on low for 8 hours. Shred and combine with the sauce and serve on sandwich bun.
PRESSURE COOKING: Place the chicken and marinade plus 1/2 cup water into the pressure cooker. Pressure cook on HIGH for 25 minutes. Shred and combine with the sauce and serve on sandwich bun.
GRILLING: Grill the chicken with marinade over direct heat for 8 to 10 minutes per side, or until cooked through. Discard any extra marinade.
Serve Nashville Hot Chicken on a sandwich bun with a Cole slaw topping and favorite side dishes.