We have engineered electron-hole bilayers of inverted InAs/GaSb quantum wells, using dilute silicon impurity doping to suppress residual bulk conductance. We have observed robust helical edge states with wide conductance plateaus precisely quantized to 2e2/h in mesoscopic Hall samples. On the other hand, in larger samples the edge conductance is found to be inversely proportional to the edge length. These characteristics persist in a wide temperature range and show essentially no temperature dependence. The quantized plateaus persist to a 12 T applied in-plane field; the conductance increases from 2e2/h in strong perpendicular fields manifesting chiral edge transport. Our study presents a compelling case for exotic properties of a one-dimensional helical liquid on the edge of InAs/GaSb bilayers.