A two-dimensional topological insulator (2DTI) is guaranteed to have a helical 1D edge mode in which spin is locked to momentum, producing the quantum spin Hall effect and prohibiting elastic backscattering at zero magnetic field. No monolayer material has yet been shown to be a 2DTI, but recently the Weyl semimetal WTe2 was predicted to become a 2DTI in monolayer form if a bulk gap opens. Here, we report that at temperatures below about 100 K monolayer WTe2 does become insulating in its interior, while the edges still conduct. The edge conduction is strongly suppressed by in-plane magnetic field and is independent of gate voltage, save for mesoscopic fluctuations that grow on cooling due to a zero-bias anomaly which reduces the linear-response conductance. Bilayer WTe2 also becomes insulating at low temperatures but does not show edge conduction. Many of these observations are consistent with monolayer WTe2 being a 2DTI. However, the low temperature edge conductance, for contacts spacings down to 150 nm, is below the quantized value,
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