Prepare the Chicken Marinade:

• Puree garlic, soy sauce, lime juice, olive oil, cumin, paprika, oregano, and a pinch of black pepper in a blender.
• Put the chicken thighs in a large Ziploc bag and pour in the marinade. Seal the bag and massage the marinade into the chicken. Refrigerate for 8 to 24 hours.

Make the Green Sauce:

• Combine all ingredients (except the olive oil) in a blender and process until smooth.
• With the motor running, slowly drizzle in the olive oil until the sauce is creamy.
• Transfer the sauce to a bowl and refrigerate until ready to serve.

Grill the Chicken:

• Preheat the grill to medium-high heat (around 350°F).
• Remove the chicken from the marinade, shaking off any excess.
• Place the chicken on the grill grates and cook for 5-6 minutes with the grill cover closed to maintain heat.
• Flip the chicken thighs using tongs and cook for an additional 5-6 minutes, or until the internal temperature reaches 165°F using a digital thermometer.

Alternative Oven Method:

• Preheat the oven to 500°F.
• Place the marinated chicken pieces in a 13×9-inch roasting pan. Add 1 cup of water to the pan.
• Bake uncovered for 30 minutes, then tent the pan with foil and continue cooking for an additional 15 minutes, or until the internal temperature reaches 165°F.

Serve:

• Serve the grilled or baked chicken with the creamy green sauce on the side.