Physical systems with non-trivial topological order find direct applications in metrology (Klitzing
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Abstract et al 1980Phys .Rev. Lett .45 494–7) and promise future applications in quantum computing (Freedman 2001Found. Comput. Math. 1 183–204; Kitaev 2003Ann. Phys. 303 2–30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system’s topology (Laughlin 1981Phys. Rev. B23 5632–33). At magnetic fields beyond the reach of current condensed matter experiment, around T, this conductance remains precisely quantized with values based on the topological order (Thoulesset al 1982Phys. Rev. Lett. 49 405–8). 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 .5 56; Miyakeet al 2013Phys. Rev. Lett. 111 185302; Aidelsburgeret al 2013Phys. Rev. Lett. 111 185301; Celiet al 2014Phys. Rev. Lett. 112 043001; Stuhlet al 2015Science 349 1514; Manciniet al 2015Science 349 1510; Anet al 2017Sci. 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 , and show that although band topology is only properly defined in infinite systems, its signatures are striking even in nearly vanishingly thin systems.