1In a food processor fitted with the metal blade or in a blender, combine the onion, garlic, lemon juice, paprika, cayenne, the 1/2 teaspoon black pepper and the thyme. Use rapid on-off pulses to combine well. Add the yogurt and pulse to mix.
Rinse the chicken and pat dry. Cut into 1-inch cubes and place in a nonaluminum container. Pour the yogurt mixture over the chicken and turn to coat. Cover and let marinate in the refrigerator for 8 hours.
Prepare a fire in a charcoal grill or preheat a broiler.
Remove the chicken pieces from the marinade, reserving the marinade, and thread them onto metal skewers. Brush the chicken with olive oil and then sprinkle with salt and pepper.
Place the skewers on an oiled grill rack or a broiler pan and grill or broil, turning and basting once with the reserved marinade, until no longer pink in the center when cut into with a knife, 4-5 minutes per side for breast meat and 5-6 minutes per side for thigh meat.
Transfer the skewers to warmed individual plates or a platter. Serve hot.