In a bowl, combine olive oil, lime juice, minced garlic, ground cumin, paprika, salt, and black pepper. Whisk until well blended.
Place the chicken breasts in a resealable plastic bag or shallow dish and pour the marinade over the chicken. Seal the bag or cover the dish and refrigerate for at least 30 minutes, or up to 4 hours for more flavor.
Preheat the grill to medium-high heat. Remove the chicken from the marinade and discard the marinade. Grill the chicken for about 6-7 minutes per side, or until the internal temperature reaches 165°F. Remove from the grill and let rest for 5 minutes before slicing.
In a large bowl, combine the mixed salad greens, cherry tomatoes, avocado, red onion, and cilantro. Toss gently to combine.
Slice the grilled chicken and arrange it on top of the salad. Sprinkle with feta cheese if desired. Serve with lime wedges on the side.