In a food processor, whirl mayonnaise, lime juice, chipotle chiles, and 1/2 tsp. salt until smooth. Chill until ready to use.
In a large bowl, using your hands, gently mix ancho chiles, cumin, oregano, remaining 1 tsp. salt, and the pepper into ground chuck. Form mixture in 4 patties 1/2 to 3/4 in. thick, then chill.
Heat a grill to high (450° to 550°). Cut onion into 4 slices, discarding ends; rub slices with oil. Lay slices on grill, close lid, and cook, turning once, until browned and slightly tender when pierced, 6 to 8 minutes total. Transfer to a platter.
Wipe cooking grate with oiled paper towels. Lay patties on grate, close lid, and cook, turning once, until don't to your liking (6 to 8 minutes total for medium, still slightly pink in the center; cut one to test). Just before burgers are done, lay hamburger buns split side down on grate and toast until lightly browned. Transfer to platter and fill with burgers and onions. Serve with chipotle mayo, along with lettuce, tomatoes, and avocados.
Note: Nutritional analysis is per serving with 2 tbsp. Chipotle Mayo.