Puree the garlic, soy sauce, lime juice, olive oil, cumin, paprika, oregano, and a pinch of black pepper in a blender for the chicken marinade.
Place chicken thighs in a large Ziploc bag, pour in the marinade, seal, and refrigerate to marinate for 8 to 24 hours.
For the green sauce, blend jalapeños, cilantro, green onions, garlic, mayonnaise, Greek yogurt, lime juice, salt, and black pepper until smooth. While blending, slowly add olive oil until incorporated. Refrigerate until serving.
To grill, preheat grill to medium-high (around 350°F). Remove chicken from marinade, shaking off excess. Grill for 5-6 minutes per side, or until internal temperature reaches 165°F.
Alternatively, bake in a preheated 500°F oven in a 13x9 inch pan with 1 cup water for 30 minutes uncovered, then covered with foil for 15 more minutes, or until fully cooked.
Prep Time: 8-24 hours for marinating + 20 minutes | Cooking Time: 10-45 minutes | Total Time: 8.5-25 hours | Servings: 4