In a bowl, whisk together Greek yogurt, olive oil, garlic, cumin and cayenne pepper.
Season both sides of chicken with a pinch of salt and pepper. Add the chicken to the marinade, cover and put in the refrigerator at least 30 minutes, an hour is even better.
Heat an outdoor grill or indoor grill pan. Once heated, add chicken. Place lemon halves (cut side down) on the grill as well. Grill 6-8 minutes per side depending on thickness of the chicken. Check the internal temp is at 165 F.
Remove from heat, squirt lemon juice on each chicken breast for added flavor.