Arrange a rack in the middle of the oven and heat the oven to 400°F.

Pat chicken thighs dry with paper towels and season all over with kosher salt. Place skin-side down in an unheated large cast iron or oven-safe skillet. Sear undisturbed until the skin is golden-brown and releases easily from the pan, 17 to 20 minutes.

Meanwhile, finely grate the zest from 1 medium lime into a small bowl. Juice the lime into the same bowl. Cut the remaining lime into wedges and reserve for serving. Peel and finely grate the ginger until you have 1/2 teaspoon, then add to the bowl with lime zest and juice. Add sweet chili sauce to the bowl and whisk to combine.

Transfer the chicken skin-side up to a plate. Pour off all but 1 tablespoon of the fat from the pan. Return the chicken to the skillet skin-side up. Pour the glaze evenly over the top.

Transfer the skillet to the oven and roast, spooning some of the glaze back over the chicken halfway through, until the internal temperature of the thickest part of the chicken registers at least 165°F, 10 to 12 minutes total.

If desired, turn the oven to broil and broil until the glaze bubbles and starts to brown, 1 to 3 minutes. Serve with reserved lime wedges.