Remove tenders from chicken breasts; set aside.
Place breasts between sheets of waxed paper or plastic wrap and pound with a meat mallet or rolling pin to a thickness of ¼ inch. Trim to shape nicely; reserve trimmings.
Mince onion and grate zest from lime; set aside.
Cut lime in half and squeeze juice over chicken breasts, rubbing to cover each well. Sprinkle with dried thyme; set aside.
Finely chop the tenders and trimmings; sauté in 1 tablespoon butter until no longer pink.
Add onion and cook until tender. Add crab meat and toss gently until warmed through. Remove pan from heat and set aside; keep warm.
Sprinkle the chicken breasts with salt and pepper; sauté in the remaining butter until lightly browned on each side. Remove to serving plates.
Stir reserved grated lime zest into the hollandaise sauce.
Spoon ¼ the crab meat mixture over each breast. Nap with hollandaise sauce.
Serve immediately with remaining sauce on the side.