Food on a stick is just more fun—especially when it comes with a peanuty, lime-spiked sauce. (And smoked paprika makes these step off from the usual satay.) Chicken thighs won’t dry out the way breasts can and have much more flavor.
Whisk together coconut milk, paprika, salt, turmeric, and 1 tablespoon lime juice in a medium bowl. Reserve 2 tablespoons marinade. Add chicken to remaining marinade, and stir to coat. Cover and chill at least 30 minutes or up to 12 hours. (If chicken marinates for more than 30 minutes, refrigerate reserved marinade.)
Meanwhile, soak skewers in hot water, 15 minutes.
Heat a grill pan over medium-high. Remove chicken from marinade, shaking off excess, and discard remaining marinade. Thread chicken onto soaked skewers. Working in batches, cook chicken skewers in hot grill pan until lightly charred and cooked through, about 5 minutes per side.
Whisk together peanut butter, 1/4 cup hot water, reserved 2 tablespoons marinade, and remaining 1 tablespoon lime juice in a medium bowl until smooth. Serve skewers with peanut sauce and lime wedges; garnish with cilantro.