Marinate the chicken. Whisk together all the marinade ingredients in a large mixing bowl. Add the chicken and toss to coat. Cover, refrigerate, and marinate for at least 30 minutes, up to 24 hours.
Make the dressing. Combine all the ingredients in a mason jar. Seal and shake really well for about 1 minute, until the dressing is emulsified. Alternately, you can combine all the ingredients in a blender and blend for 10-20 seconds.
Grill the chicken. Preheat a grill or grill pan over medium heat. Remove the chicken from the marinade and grill for 5-6 minutes per side, until chicken is cooked through. It should register 165 F as an internal temperature. Let the chicken rest, then slice.
Assemble the salad. Divide the lettuce among bowls with the tomatoes, cucumber, red onion, olives, pepperoncini, and feta. Top with grilled chicken and drizzle with desired amount of dressing. Serve immediately.