Heat your grill up on high for at least 10 minutes before you want to start grilling.
In a high-speed blender, add the herbs, oil, vinegar, salt, pepper, and garlic. Blend until smooth, starting at a lower speed and increasing to high.
In a large bowl, add the chicken thighs, tomatoes, and zucchini. Add a scant ¼ cup of the chimichurri to the bowl and use your hands to toss to coat thoroughly.
Assemble the veggies on skewers or add them to a grill pan. Place the chicken and veggies on the grill and cook, covered, for 10 minutes, flipping the chicken and rotating the veggies halfway through or until the chicken thighs have nice grill marks and veggies are beginning to char/are cooked through.
In a medium bowl, mix together the yogurt and remaining chimichurri.
Serve the chicken and veggies on a large platter with yogurt chimichurri sauce on the side and/or drizzled over top.