| 4 boneless, skinless chicken breast halves (8 ounces each), gently pounded to an even thickness |
| 1/4 cup extra-virgin olive oil, plus 1 teaspoon for drizzling |
| 1/4 cup lime juice (from 4 limes), plus 1 teaspoon for drizzling |
| 3 cups tender greens, such as mache or baby lettuces |
| 4 radishes, very thinly sliced |