  Wireless technology relies on the conversion of alternating electromagnetic
fields to direct currents, a process known as rectification. While rectifiers
are normally based on semiconductor diodes, quantum mechanical non-reciprocal
transport effects that enable highly controllable rectification have recently
been discovered. One such effect is magnetochiral anisotropy (MCA), where the
resistance of a material or a device depends on both the direction of current
flow and an applied magnetic field. However, the size of rectification possible
due to MCA is usually extremely small, because MCA relies on inversion symmetry
breaking leading to the manifestation of spin-orbit coupling, which is a
relativistic effect. In typical materials the rectification coefficient
$\gamma$ due to MCA is usually $|\gamma| \lesssim 1$ ${\rm A^{-1} T^{-1}}$ and
the maximum values reported so far are $|\gamma| \sim 100$ ${\rm A^{-1}
T^{-1}}$ in carbon nanotubes and ZrTe$_5$. Here, to overcome this limitation,
we artificially break inversion symmetry via an applied gate voltage in thin
topological insulator (TI) nanowire heterostructures and theoretically predict
that such a symmetry breaking can lead to a giant MCA effect. Our prediction is
confirmed via experiments on thin bulk-insulating
(Bi$_{1-x}$Sb$_{x}$)$_2$Te$_3$ TI nanowires, in which we observe an MCA
consistent with theory and $|\gamma| \sim 100000$ ${\rm A^{-1} T^{-1}}$, the
largest ever reported MCA rectification coefficient in a normal conductor.
