Combine olive oil, balsamic vinegar, Dijon mustard, salt, and pepper.
Marinate chicken breasts in this mixture for at least two hours in the refrigerator.
Preheat a griddle pan over medium-high heat and cook the chicken until it is half done.
This usually takes about 5 minutes on each side.
Flip the chicken over, and then baste with the French Mustard Vinaigrette.
Continue cooking until fully done.
While the chicken cooks, heat a sauté pan over medium-high heat.
Add grape tomatoes, artichoke hearts, and capers.
Cook for about 2 minutes.
Serve the cooked chicken with the vegetable mixture on top.
Garnish with freshly chopped basil for a bright finish.