In a shallow dish, whisk together the yogurt, olive oil, garlic, kosher salt, black pepper, paprika, cumin, and cayenne.
Add the chicken, turning it to make sure it's well-coated.
Set aside to marinate for 30 minutes, or cover, place in the fridge and marinate for a few hours.
Heat a grill, dual-contact grill, or grill pan on high heat, about 5 minutes, and lightly grease it. Grill the chicken breasts for 4-6 minutes on each side, or for a total of 4-6 minutes on a dual-contact grill, until juicily cooked through and an instant-read thermometer inserted into the thickest part registers 165 degrees F.
Rest the chicken for 5-10 minutes before slicing and serving.
This recipe was written for small 6oz chicken breasts. If yours are larger, they'll need more time on the grill, and if so, it's best to reduce the heat to medium after the initial 6 minutes so that they don't burn. You can use plain whole-milk yogurt instead of Greek yogurt. The marinade won't be as thick, but that's not a bad thing. It actually might be easier to work with.