Finely grate the zest of the lemon, lime and orange into a medium bowl. Squeeze in the juice of each fruit. Add the chili powder, adobo seasoning and olive oil; whisk to combine. Add the chicken and coat well with the marinade; cover and refrigerate for at least 1 hour or overnight.
Preheat a grill or grill pan to medium-high. Grill the chicken breasts until cooked through, about 8 minutes per side, turning once. Move the chicken to the cooler side of the grill (or reduce the heat on the stove) and top each piece with 1 tablespoon salsa and 1 slice cheese. Cover and cook until the cheese melts, 1 to 2 minutes. Place a chicken breast on each roll bottom; add a few slices of avocado and cover with the roll top. Serve with more salsa, if desired.