In a high-powered blender, combine garlic, shallot, salt, lime zest, cumin, oregano, black pepper, orange juice, lime juice, and olive oil. Blend until the marinade is completely smooth.
Pour ⅓ cup of the marinade into a small bowl and reserve it for the dipping sauce later.
Place the chicken thighs in a large bowl or zip-top bag and pour the remaining marinade over the chicken. Coat well.
Cover and refrigerate for at least 1 hour, or up to 24 hours for deeper flavor.
Preheat a grill to medium-high heat and lightly oil the grill grates.
Place the chicken on the grill and allow it to char for 30–60 seconds. Reduce heat to medium-low.
Grill the Cuban Mojo Chicken for 10–15 minutes, turning every 5–7 minutes, until the internal temperature reaches 165°F.
While the chicken cooks, pour the reserved marinade into a small non-stick skillet and simmer over medium-high heat for 3–5 minutes until slightly thickened.
Drizzle the reduced mojo sauce over the grilled chicken and serve warm.