a horse race over a racecourse with hedges and ditches for jumping: compare flat race, hurdle1 (2b)
archaic a horse race across country with hedges, walls, ditches, etc to jump
a middle-distance running race over obstacles, strictly one of 3000m over 28 hurdles and seven water jumps
steeplechaser noun
steeplechasing noun
[from the use of church steeples as landmarks to guide the riders]