Preheat the oven to 350 degrees F.
Heat a large nonstick oven proof skillet over medium-high heat. Add the olive oil and swirl to coat the skillet. Season the chicken breast with salt and pepper on the smooth side of each breast. Place in the skillet seasoned side down and cook without disturbing until brown and crisp, about 3 to 4 minutes. Season the top side of the chicken and flip. Cook 1 minute over the burner; then transfer the skillet to the oven until the chicken registers 165 on an instant-read thermometer, about 8 to 10 minutes more. Set chicken aside to rest for 5 minutes before serving.
Divide the romaine, celery, radishes, and feta among 4 plates. Drizzle about 3/4 of a tablespoon of the olive oil over each salad, season with salt and pepper and serve with a lemon wedge.
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