In a large bowl, whisk together the olive oil, minced garlic, smoked paprika, cumin, lime juice, salt, and pepper. Add the chicken thigh pieces and toss to coat. Cover and marinate in the refrigerator for at least 30 minutes, or up to 4 hours for best flavor.
Meanwhile, make the chimichurri. Combine the parsley, cilantro, oregano, garlic, and red pepper flakes in a food processor and pulse until roughly chopped. Add the red wine vinegar and olive oil and pulse again until combined but still slightly textured — you want a sauce, not a purée. Season with salt and pepper. Transfer to a bowl and set aside. The chimichurri can be made up to 24 hours ahead.
If using wooden skewers, soak them in water for at least 30 minutes before grilling.
Thread the marinated chicken pieces onto the skewers, alternating with pieces of red bell pepper, yellow bell pepper, and red onion.
Preheat the grill to medium-high heat. Grill the skewers for 5–6 minutes per side, until the chicken is cooked through and has beautiful char marks and the vegetables are tender and slightly caramelized.
Transfer to a serving platter. Drizzle generously with chimichurri and serve the remaining chimichurri on the side for dipping.