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.