In a bowl, combine olive oil, lime juice, cumin, paprika, salt, and black pepper. Add chicken thighs and coat well. Marinate for at least 30 minutes.

In a blender, combine cilantro, jalapeño, garlic, lime juice, mayonnaise, and salt. Blend until smooth. Add water to thin if necessary.

In a pot, bring water to a boil. Add rice and salt. Reduce heat, cover, and simmer for 18 minutes. Remove from heat and let sit for 5 minutes. Fluff with a fork and stir in chopped cilantro.

Preheat the grill to medium-high heat. Grill the marinated chicken for about 6-7 minutes per side or until the internal temperature reaches 165°F (75°C).

Serve the grilled chicken with cilantro rice and drizzle with Aji Verde sauce.