Place chicken thighs into a gallon-sized resealable plastic bag. Blend soy sauce, garlic, lime juice, vegetable oil, cumin, paprika, and oregano in a blender until smooth. Pour mixture over chicken, seal the bag, and refrigerate for 8 hours.
Combine jalapeno peppers, cilantro, mayonnaise, lime juice, olive oil, garlic, salt, and pepper in a blender; pulse until sauce is smooth. Transfer sauce to a covered bowl and refrigerate until ready to serve.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Remove chicken thighs from the bag and place on the grill. Discard bag with excess marinade. Grill thighs for 7 minutes; flip and grill 7 additional minutes.
Transfer thighs to a serving dish and drizzle reserved sauce over the chicken.
