Make the Peanut Sauce: Heat the oil in a small saucepan over high heat until hot. Add the curry paste and cook, stirring, until very fragrant and thick, about 1 minute.
Stir in the coconut milk; bring to a boil and cook, stirring constantly, for 2 minutes. Be careful not to let it boil over. Add the peanut butter and cook, stirring constantly, until the sauce begins to thicken and come together, 2 to 3 minutes.
Reduce the heat to a simmer and add the fish sauce, sugar and rice vinegar. Cook, stirring, until the ingredients are incorporated, about 1 minute more; remove from the heat. An oily film will rise to top; skim it off, if you wish. Keep the sauce warm while you make the chicken satay. (See Cook's Note.)
Make the Chicken Satay: Place the coconut milk, curry powder, salt, sugar, pepper and garlic powder in a medium bowl; whisk to combine the marinade.
Slice the chicken against the grain into 2-inch square tiles about 1/4-inch thick. Transfer to the marinade and massage to coat the chicken evenly. You can cover and marinate the chicken overnight in the refrigerator for better flavor and tenderness or cook it immediately.
Thread the chicken onto the bamboo skewers, stopping 2 inches from the bottom of each skewer.
Heat a grill or grill pan to high and preheat for at least 5 minutes. Rub a little oil on the grill grates or spray with nonstick cooking spray. Working in batches if necessary, grill the chicken on one side until you get nice char marks, 3 to 5 minutes. Flip and cook until the chicken is just cooked through, another 3 to 5 minutes. Serve the chicken satay with the peanut sauce on the side for dipping.
The peanut sauce can be refrigerated for up to 5 days. Rewarm before serving, stirring in a few tablespoons of hot water if it's too thick.