In a medium bowl, whisk together the mustard, apple juice, vinegar, 2 tablespoons water, 1/4 teaspoon of the pepper, and 1/2 cup of the oil. Transfer 1/2 cup of the mixture to a large resealable plastic bag and refrigerate the rest.
Rinse the chicken and pat dry with paper towels. Add to the bag, seal, and refrigerate for 20 minutes.
Meanwhile, heat grill to medium. Place the zucchini, tomatoes, and onion on a baking sheet. Add the salt and the remaining oil and pepper and toss. Grill the chicken and vegetables, turning occasionally, for about 10 minutes total. Transfer to a cutting board and roughly chop the ingredients. Divide the salad greens among individual bowls and top with the chicken, vegetables, and the reserved dressing.
Tip: You can vary the vegetables depending on what's plentiful at the farmers' market or in your vegetable bin. Asparagus and sliced bell peppers taste terrific with the vinaigrette and take approximately the same amount of time to grill.