In a large mixing bowl, whisk together olive oil, lemon juice (about 1/4 cup), lemon zest, salt and pepper.
Place chicken in the bowl and marinate in the refrigerator for at least 30 minutes.
To make the dipping sauce, in a medium bowl, whisk together yogurt, garlic, Dijon mustard, lemon juice and lemon zest. Season with salt and pepper, to taste.
Prepare grill for direct grilling over medium-high heat.
Brush and oil the grill grate.
Place the chicken on the grill directly over the fire and cook until the juices run clear and the chicken is cooked through, about 5 to 8 minutes on each side.
Serve grilled chicken with lemon yogurt dipping sauce and your favorite side dish (I love citrus grilled or roasted asparagus).