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1
Brine the chicken:
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2
In a large bowl, combine 2 cups boiling water with the sugar and salt and stir to dissolve. Let cool completely. Add the chicken breasts, cover, and refrigerate for 2 to 3 hours.
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3
Make the chile oil:
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4
In a medium skillet, lightly toast the cumin, coriander, and caraway seeds over medium heat, stirring often, until fragrant, about 2 minutes. Grind the seeds to a powder in an electric spice grinder and transfer to a medium bowl. In the same skillet, toast the chiles over medium heat, pressing on them with a spatula, until fragrant and darker in spots, about 1 minute per side. Remove the stems and seeds and grind in the spice grinder-you'll need 3 Tbs. ground chile. Add the ground chile, cayenne, garlic, and 1 tsp. salt to the ground spices, and then stir in the oil and vinegar. Taste and adjust the seasoning with more salt or vinegar if necessary. Stir before using.
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5
Grill the chicken:
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6
Prepare a medium gas or charcoal grill fire. While the grill heats, remove the chicken from the brine, pat dry with paper towels, and let sit at room temperature.
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7
Toss the chicken with 2 Tbs. of the chile oil. Grill the chicken without moving until golden brown grill marks form, 4 to 6 minutes. Flip the chicken and grill until just cooked through, 4 to 5 minutes. Transfer to a cutting board and let rest for a few minutes. Holding your knife at an angle, cut the breasts crosswise into 1/2 -inch-thick slices and let cool to room temperature. Serve with the remaining chile oil on the side.