Step 1

To make the marinade: Slice the pineapple crosswise into 1-inch-thick rounds. Using a paring knife, remove the  core from each round (this can be done roughly,  since the core is edible). Chop half the pineapple coarsely; set aside the remaining half for the relish. Add the chopped pineapple to a blender, together with the jalapeño, onion, vinegar, garlic, and salt and blend until smooth. Transfer the marinade to a bowl, add the chicken breasts, and refrigerate, covered, for at least 8 hours or up to 24 hours.

Step 2

Wipe the grill grates with oil to prevent sticking. Build a two-zone fire. Your high-heat zone should have embers 1 to 2 inches from the cooking surface, with occasional flames licking it. To create your medium-heat zone, nudge the embers 2 to 3 inches lower than that.

Step 3

To make the relish: Toss the remaining pineapple in oil, honey, and salt to coat. Grill over medium heat until itis nicely caramelized, about 3 minutes per side. Meanwhile, grill the jalapeño and onion over medium heat until lightly charred, turning often, about 3 minutes for the jalapeño and 8 minutes for the onion. As they finish cooking, transfer the pineapple, jalapeño, and onion to a cutting board.

Step 4

When they are cool enough to handle, coarsely chop the pineapple, jalapeño, and onion and add to a bowl with the vinegar, 1 tablespoon honey, and cilantro. Season with more salt, and add more vinegar or honey, if needed. Set aside until ready to serve.

Step 5

Remove the chicken breasts from the marinade, shaking off any excess, and bring to room temperature. Place skin side down over high heat. After about 90 seconds, using tongs, rotate 45 degrees and cook for another 2 minutes. Flip the breasts and do the same on the other side. Once you have nice grill marks on both sides, move to medium heat and cook, turning often, until an instant-read meat thermometer, placed in the thickest part of a breast, reads 160ºF on a meat thermometer. Transfer to a cutting board and let the breasts rest for 10 minutes before slicing and serving with the relish.