What LEGO set has the biggest box?
As far as regular sets go (ie. no furniture or big-boxes like that Chima combo), the current UCS Millennium Falcon does appear to be the largest box by total volume.

75192-1 Millennium Falcon - UCS (2nd edition)

54 x 45 x 39 cm = 94770 cm3

54 x 45 cm = 2430 cm2



The original UCS Millennium Falcon box was actually larger in 2 directions however, though the total volume is smaller.

10179-1 Millennium Falcon - UCS

64.39 x 47.63 x 19.69 cm = 60387.176333 cm3

64.39 x 47.63 cm = 3066.8957 cm2



There appear to be a number of sets that are larger in at-least one direction, see this answer for the longest one identified so-far.