In a large bowl, whisk together the vinegar, oil, mustard, brown sugar, garlic, Italian seasoning, and lemon juice. Season the marinade to taste with salt and pepper.
Brush some of the marinade over the corn cobs; set aside. Add the chicken to the bowl with the remaining marinade and turn to coat. Cover and let sit 1 hour.
Heat your grill to medium high. Add the chicken and and corn over direct heat and cook for 10-15 minutes, or until the chicken is cooked through and the corn is lightly charred (the corn should be done after 10 minutes). Remove from the grill and let cool slightly. When the corn is cool enough to handle, cut the kernels away from the cob.
Spread the salad greens over a large platter. Top with grilled chicken, corn, tomatoes, mozzarella, and croutons. Serve with pesto vinaigrette.