Overall, I agree with my friend olly. "A" space to me implies one specific measurement--that is, the spaces between all the chairs are equivalent; but, implies only: I can't argue with somebody saying the spaces are of different measurements.

between the chairs could mean not necessarily all of the chairs; saying each chair removes that possibility.

Depends on what you want to convey, I reckon. If I heard, "The crew set up the auditorium so that there is space between the chairs", I would assume that it meant that none of the chairs touched another.