Preheat an indoor or outdoor grill to medium-high. Brush the chicken with the oil; season with chili powder, cumin, salt and pepper. Grill 3 to 4 minutes per side, or until cooked through. Cool the chicken a few minutes and then slice.
Spread one side of each bread slice with mayonnaise. Top the mayonnaise on 4 of the slices with an equal amount of lettuce, tomatoes, sliced chicken and bacon. Set on the remaining bread slices, mayonnaise side down. Cut each sandwich in half and serve.