Start by whisking together all the marinade ingredients including the soy sauce, garlic, lime juice, paprika, cumin, oregano and black pepper. Add in the chicken and toss to coat in the marinade.
Heat the grill to medium high heat. Once the grill is heated, add the chicken pieces and cook for 6-8 minutes per side.
While the chicken is grilling, combine the cilantro, jalapeno, garlic, mayo, lime juice and vinegar in a blender. Slowly pour in the olive oil.
Once the chicken is cooked through, remove it from the grill and serve with the green sauce. Either drizzle it over the chicken, or serve it on the side as a dipping sauce.