  We construct a string theory realization of the 4+1d quantum Hall effect
recently discovered by Zhang and Hu. The string theory picture contains
coincident D4-branes forming an S^4 and having D0-branes (i.e. instantons) in
their world-volume. The charged particles are modelled as string ends. Their
configuration space approaches in the large n limit a CP^3, which is an S^2
fibration over S^4, the extra S^2 being made out of the Chan-Paton degrees of
freedom. An alternative matrix theory description involves the fuzzy
four-sphere. We also find that there is a hierarchy of quantum Hall effects in
odd-dimensional spacetimes, generalizing the known cases in 2+1d and 4+1d.
