In a large mixing bowl, whisk together the Thai red curry paste, unsweetened coconut milk, fish sauce, brown sugar, and lime juice until the marinade is smooth and fully combined.

Add the cubed chicken thighs to the bowl, tossing thoroughly to ensure every piece is coated in the marinade, then cover and refrigerate for at least 30 minutes.

While the chicken marinates, soak wooden skewers in water for 30 minutes to prevent them from burning, or prepare metal skewers.

Thread the marinated chicken, red bell pepper, and red onion pieces alternately onto the skewers, leaving a little space at the ends for handling.

Preheat your outdoor grill or indoor grill pan to medium-high heat and lightly brush the grates with vegetable oil using a paper towel and tongs.

Grill the kebabs for 12 to 15 minutes, turning every few minutes, until the chicken is nicely charred on the edges and has reached an internal temperature of 165 degrees Fahrenheit.

Transfer the hot kebabs to a serving platter, let them rest for 3 minutes, and serve immediately with fresh lime wedges and a garnish of chopped cilantro.