In the bowl of a food processor fitted with the metal blade, place all the herbs and the garlic. Process until well chopped. Transfer to a medium bowl. Add remaining sauce ingredients to the herbs and combine well.
Place the cubed chicken in a non-reactive container and add a few spoonfuls of chimichurri sauce and toss to coat. Cover and refrigerate chicken up to overnight or allow chicken marinate at room temperature for 1 hour. Cover and refrigerate reserved sauce.
Heat a grill over medium heat until hot. Drizzle the vegetables lightly with olive oil. Thread the chicken onto skewers alternating with vegetables. If using wooden skewers, use two skewers per kabob, that way the chicken won’t turn around the skewer as you flip. Season kabobs lightly with sea salt. Grill on both sides until chicken is cooked through, about 5-6 minutes per side. Serve with reserved chimichurri sauce on the side.