Heat the grill to medium heat (375–400 °F / 190–200 °C).
Use a sharp knife to slice each chicken breast horizontally, creating a pocket deep enough to hold the fillings but still leaving it mostly intact.
Squeeze fresh lime juice over both sides of each chicken breast. Season with salt and pepper to taste.
Into each breast, place several jalapeño slices and 4–5 asparagus stalks.
Wrap each stuffed breast in 2 strips of bacon, wrapping snugly. Sprinkle about 1 tablespoon of brown sugar evenly over the bacon-wrapped chicken.
Insert a barbecue skewer lengthwise through the entire bundle. Cook for about 25 minutes, turning once or twice, until the chicken reaches an internal temperature of 165 °F (74 °C) and the bacon is crispy. If the bacon drips cause flare-ups, move the chicken to a cooler part of the grill for a minute.
Remove from the grill and let the chicken rest for a few minutes before slicing or serving. This keeps the juicy, flavorful filling intact.
Notes
Oven method: Heat the oven to 400°F (200°C). Place the stuffed, bacon-wrapped breasts on a wire rack set inside a foil-lined rimmed baking sheet (secure with toothpicks if skewers don't fit) and bake for 30 to 35 minutes, until the chicken reaches 165°F (74°C). Broil for 1 to 2 minutes for extra-crispy bacon, watching closely.Bacon: Regular-cut bacon crisps better than thick-cut on the grill.Storage: Refrigerate leftovers in an airtight container for up to 3 days, or freeze for up to 3 months. Reheat in a 350°F (175°C) oven for 12 to 15 minutes.