Preheat your grill or a grill pan over medium-high heat.
In a small bowl, mix together the olive oil, black pepper, garlic powder, onion powder, and salt. Rub this mixture all over the chicken breasts.
Grill the chicken for about 6-7 minutes on each side, or until fully cooked and the internal temperature reaches 165°F. Remove from heat and let rest for 5 minutes before slicing.
While the chicken is resting, prepare the salad. In a large bowl, combine the radishes, cucumber, cherry tomatoes, red onion, and parsley.
In a small bowl, whisk together the lemon juice and balsamic vinegar. Pour over the salad and toss to combine.
Slice the grilled chicken and serve it on top of the salad.