Step 1

Generously season chicken halves all over with salt (use about 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt per pound of chicken) and pepper. Let sit at room temperature at least 15 minutes, or chill up to 1 day. If chilling, let sit at room temperature 1 hour before grilling.

Step 2

Whisk marmalade, mustard, vinegar, soy sauce, jalapeño (if using), and garlic in a small bowl to combine. Set glaze aside.

Step 3

Prepare a grill for medium-high indirect heat (for a charcoal grill, bank coals on one side of grill; for a gas grill, leave one or two burners off). Lightly oil grate. Pat chicken dry with paper towels, then rub with 1 Tbsp. oil. Place, skin side down, over indirect heat. Cover grill and grill chicken, turning halfway through, until skin is lightly browned and an instant-read thermometer inserted into thickest part of thighs registers 120°–130°, 15–20 minutes.

Step 4

Uncover grill, turn chicken over, and move over direct heat. Brush chicken with reserved glaze. Grill, turning often and brushing generously with glaze (move to indirect heat if browning too quickly), until charred in spots and an instant-read thermometer inserted into thickest part of breast registers 150° (it will climb to 160° as chicken rests), 10–15 minutes. Transfer chicken, skin side up, to a cutting board; let rest 15 minutes.

Step 5

While chicken is resting, transfer any remaining glaze to a small saucepan and cook over medium-high heat, stirring occasionally, until bubbling and slightly thickened, about 5 minutes.

Step 6

Carve chicken and transfer to a platter; sprinkle with sea salt. Serve with sauce alongside.