For the marinade, in a large bowl whisk together the melted butter, olive oil, lemon juice, orange juice, garlic, Dijon, oregano, salt, paprika, and black pepper. Add the chicken thighs to the marinade and marinate for 1-2 hours in the fridge, if time allows.
Preheat grill to 350°F. (medium high heat), and lightly oil the grill grates. Place the chicken on the grates. Let the chicken char for 1 minute, and then immediately reduce the heat to medium low. Grill the chicken for approximately 15 to 20 minutes, or until the internal temperature reaches 165°F, turning every 5-7 minutes.
Meanwhile, to make the basil sauce, combine all the ingredients in a blender or food processor and blend until smooth. Season to taste.
Transfer the chicken to a platter, drizzle with basil sauce all over, and garnish with fresh basil leaves and serve with fresh lemon wedges. Enjoy!