Cut the chicken breasts into 1-inch pieces and place in a large bag, or bowl.
In a separate bowl or liquid measuring cup, whisk together the olive oil, vinegar, honey, garlic, oregano, salt, and pepper.
Pour over the chicken and stir. Place in the refrigerator to marinate for 30 minutes or up to 3 hours (do not let the chicken sit for longer or the vinegar will cause it to break down). If using wooden skewers, place the skewers in water to soak for at least 20 minutes.
Preheat the grill to medium-high heat (about 375 degrees F). Brush the grill grates with vegetable oil.
Thread a piece of chicken onto the skewer. Add alternating pieces of the red onion, zucchini, yellow squash, and red bell pepper until you’ve reached the end of the skewer, ending with chicken.
Grill the chicken until fully cooked through and the juices run clear, about 10 to 15 minutes, turning the skewers every few minutes so that each side has grill marks. Make sure that it is cooked by checking it with the thermopro thermometer.
Transfer to a serving plate and squeeze the lemon over the top. Serve warm on your board.