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1
Place the coconut milk, fish sauce, brown sugar, curry paste, and salt in a large bowl and whisk to combine; set aside.
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2
Cut the chicken lengthwise into 1/2-inch-thick pieces and add to the marinade.
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3
Stir to coat the chicken, cover the bowl with plastic wrap, and refrigerate for at least 30 minutes or up to 24 hours.
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4
Meanwhile, make the sauce.
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5
Place everything but the lime juice in a small saucepan and whisk to combine.
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6
Bring to a simmer over medium heat, stirring occasionally, until the ingredients are evenly combined, about 3 minutes total.
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7
Remove the pan from the heat, stir in the lime juice, and transfer the sauce to a small bowl to cool.
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8
Heat a gas or charcoal grill to medium-high (about 375 degrees F to 425 degrees F).
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9
Meanwhile, thread a single piece of chicken lengthwise onto each skewer and transfer to a baking sheet.
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10
When the grill is ready, rub the grates with a towel dipped in vegetable oil.
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11
Place the skewers on the grill, close the cover, and cook until grill marks appear on the bottom, about 3 to 4 minutes.
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12
Flip the chicken, close the grill, and cook until grill marks appear on the second side and the chicken is cooked through, about 3 to 4 minutes more.
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13
Transfer the skewers to a clean serving platter and serve with the cooled peanut sauce for dipping.