In a large bowl, whisk together the coconut milk, soy sauce, lime juice, brown sugar, Thai red curry paste, garlic, ginger, salt, and pepper until smooth.
Add the chicken cubes and toss until every piece is thoroughly coated.
Cover and refrigerate for at least 1 hour, preferably overnight for maximum flavor.
Preheat the grill to medium-high heat (about 400°F / 200°C).
Remove the marinated chicken from the refrigerator and let it rest at room temperature for 10 minutes.
Thread the chicken evenly onto the soaked skewers.
Grill the Grilled Thai Coconut Chicken Skewers for 10–15 minutes, turning every few minutes until lightly charred and the internal temperature reaches 165°F (74°C).
Let the skewers rest for 2–3 minutes before serving.
Garnish with fresh cilantro, lime wedges, and sliced green onions if desired.