Heat the olive oil in a large pot over medium heat. Add the garlic and onions and cook for a few minutes until the onions soften. Add the chicken and cook until lightly browned. Add three-quarters of the beer, reserving the rest, then cook for a couple of minutes to reduce. Add the black beans, kidney beans, pinto beans, tomatoes, chile powder, cumin, salt and chipotles and stir to combine. Bring to a simmer, then cover the pot and cook for 1 hour.
Combine the masa harina with the rest of the beer and stir to make a paste. Add this into the chili, along with the lime juice. Stir and cook until thick, 10 more minutes.
Serve with the grated cheese, sour cream, diced tomatoes, cilantro and lime wedges for squeezing.