Preheat grill to medium-high.
Combine 1 tbs oil, coriander, and ¼ tsp 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 165F, 8 to 10 minutes total. Alternatively, cook the chicken in a grill pan over medium to medium-high heat.
Meanwhile, combine cucumber, tomatoes, mint, and vinegar in a medium bowl with the remaining 1 tbs oil and ¼ tsp each salt and pepper. Serve with the chicken.