1. Make a few slashes in meat side of each thigh. In a 9-by-13-inch baking dish, combine chicken and marinade, turning to coat. Refrigerate at least 1 day and up to 2 days.

2. Preheat oven to 250 degrees. In a large bowl, whisk together flour and 1 1/2 teaspoons salt; season with pepper. In a large straight-sided skillet (preferably cast iron), heat 3 cups oil (it should be about 1/2 inch deep) over medium-high until a thermometer registers 350 degrees.

3. Working with 6 pieces at a time, remove chicken from marinade, wiping off excess with a paper towel. Dredge in flour mixture and add to skillet, skin-side down. Partially cover and fry until golden brown and cooked through, 6 to 7 minutes a side. (Adjust heat to maintain oil temperature between 330 degrees and 350 degrees; do not let it go over 350 degrees, and return to 350 degrees between batches.) Transfer chicken to a paper towel-lined plate; place in oven to keep warm.

4. Mix together onion and lime juice; let stand 10 minutes. Stir in remaining 2 tablespoons oil and herbs. Season with salt. Serve chicken, with onion salad and cucumbers.