In a bowl, combine the chicken, Thai green curry paste, fish sauce, soy sauce, lime juice, and brown sugar. Mix well to combine and let marinate for 20 minutes.
Preheat a grill or grill pan over medium-high heat.
Thread the chicken, bell peppers, and red onion onto the soaked bamboo skewers, alternating between ingredients.
Grill the skewers for about 4-5 minutes per side, or until the chicken is cooked through and slightly charred.
Serve the Thai green curry chicken skewers with steamed rice or a side salad.
Enjoy!