  Physical systems with non-trivial topological order find direct applications
in metrology[1] and promise future applications in quantum computing[2,3]. The
quantum Hall effect derives from transverse conductance, quantized to
unprecedented precision in accordance with the system's topology[4]. At
magnetic fields beyond the reach of current condensed matter experiment, around
10^4 Tesla, this conductance remains precisely quantized but takes on different
values[5]. Hitherto, quantized conductance has only been measured in extended
2-D systems. Here, we engineered and experimentally studied narrow 2-D ribbons,
just 3 or 5 sites wide along one direction, using ultracold neutral atoms where
such large magnetic fields can be engineered[6-11]. We microscopically imaged
the transverse spatial motion underlying the quantized Hall effect. Our
measurements identify the topological Chern numbers with typical uncertainty of
5%, and show that although band topology is only properly defined in infinite
systems, its signatures are striking even in nearly vanishingly thin systems.
