Combine cilantro, Thai basil, fish sauce, green onions, lime juice, lime zest, brown sugar, ginger, kosher salt, and 3/4 teaspoon pepper in a medium-sized bowl.
Combine chicken thighs and cilantro mixture in a gallon-sized zip-top bag. Marinate in the refrigerator 8 hours to overnight, turning occasionally.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Drain chicken thighs and discard marinade. Season with salt and pepper to taste.
Add chicken to the preheated grill and cook until no longer pink in the centers, 7 to 10 minutes per side. An instant-read thermometer inserted into the center of each thigh should read at least 165 degrees F (74 degrees C). Serve immediately.