Combine 1 tablespoon oil, coriander and ¼ teaspoon each salt and pepper in a small bowl. Brush on both sides of chicken.
Grill the chicken, turning once, until an instant-read thermometer inserted in the thickest part registers 165°F, 8 to 10 minutes total. (Alternatively, cook the chicken in a grill pan over medium to medium-high heat.)
Meanwhile, combine cucumber, radishes, mint and vinegar in a medium bowl with the remaining 1 tablespoon oil and ¼ teaspoon each salt and pepper. Serve with the chicken.
193 calories;10 g fat(2 g sat); 1 g fiber; 2 g carbohydrates; 23 g protein; 15 mcg folate; 63 mg cholesterol; 0 g sugars; 0 g added sugars; 261 IU vitamin A; 3 mg vitamin C; 31 mg calcium; 2 mg iron; 353 mg sodium; 275 mg potassium