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Physical systems with non-trivial topological order find direct applications in metrology (Klitzinget al1980Phys.Rev. Lett.45494–7) and promise future applications in quantum computing (Freedman 2001Found. Comput. Math.1183–204; Kitaev 2003Ann. Phys.3032–30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system’s topology (Laughlin 1981Phys. Rev.B235632–33). At magnetic fields beyond the reach of current condensed matter experiment, around${\mathrm{10}}^{\mathrm{4}}$T, this conductance remains precisely quantized with values based on the topological order (Thoulesset al1982Phys. Rev. Lett.49405–8). Hitherto, quantized conductance has only been measured in extended 2D systems. Here, we experimentally studied narrow 2D ribbons, just 3 or 5 sites wide along one direction, using ultracold neutral atoms where such large magnetic fields can be engineered (Jaksch and Zoller 2003New J. Phys.556; Miyakeet al2013Phys. Rev. Lett.111185302; Aidelsburgeret al2013Phys. Rev. Lett.111185301; Celiet al2014Phys. Rev. Lett.112043001; Stuhlet al2015Science3491514; Manciniet al2015Science3491510; Anet al2017Sci. Adv.3). We microscopically imaged the transverse spatial motion underlying the quantized Hall effect. Our measurements identify the topological Chern numbers with typical uncertainty of$\mathrm{5}\%$, and show that although band topology is only properly defined in infinite systems, its signatures are striking even in nearly vanishingly thin systems.