  Sixty years ago, Karplus and Luttinger pointed out that quantum particles
moving on a lattice could acquire an anomalous transverse velocity in response
to a force, providing an explanation for the unusual Hall effect in
ferromagnetic metals. A striking manifestation of this transverse transport was
then revealed in the quantum Hall effect, where the plateaus depicted by the
Hall conductivity were attributed to a topological invariant characterizing
Bloch bands: the Chern number. Until now, topological transport associated with
non-zero Chern numbers has only been revealed in electronic systems. Here we
use studies of an atomic cloud's transverse deflection in response to an
optical gradient to measure the Chern number of artificially generated
Hofstadter bands. These topological bands are very flat and thus constitute
good candidates for the realization of fractional Chern insulators. Combining
these deflection measurements with the determination of the band populations,
we obtain an experimental value for the Chern number of the lowest band
$\nu_{\mathrm{exp}} =0.99(5)$. This result, which constitutes the first
Chern-number measurement in a non-electronic system, is facilitated by an
all-optical artificial gauge field scheme, generating uniform flux in optical
superlattices.
