Marinate the Chicken. In a bowl, combine garlic, lime juice, cumin, paprika, oregano, salt, and pepper. Add the chicken thighs and coat them well with the marinade. Cover and refrigerate for at least 1 hour.
Prepare the Aji Verde Sauce. In a blender, combine mayonnaise, jalapeños, cilantro, garlic, lime juice, salt, and pepper. Blend until smooth, adding water as needed to achieve the desired consistency. Adjust seasoning to taste.
Grill the Chicken. Preheat the grill or oven to medium-high heat. Grill the marinated chicken thighs until they are cooked through and golden brown, about 6-8 minutes per side.
Serve. Serve the grilled or roasted chicken thighs with a generous dollop of Aji Verde sauce on top. Garnish with fresh cilantro and lime wedges if desired.