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.
Remove from the grill and let the chicken rest for a few minutes before slicing or serving. This keeps the juicy, flavorful filling intact.