  A prominent feature of topological insulators (TIs) is the surface states
comprising of spin-nondegenerate massless Dirac fermions. Recent technical
advances have made it possible to address the surface transport properties of
TI thin films while tuning the Fermi levels of both top and bottom surfaces
across the Dirac point by electrostatic gating. This opened the window for
studying the spin-nondegenerate Dirac physics peculiar to TIs. Here we report
our discovery of a novel planar Hall effect (PHE) from the TI surface, which
results from a hitherto-unknown resistivity anisotropy induced by an in-plane
magnetic field. This effect is observed in dual-gated devices of
bulk-insulating Bi$_{2-x}$Sb$_{x}$Te$_{3}$ thin films, in which both top and
bottom surfaces are gated. The origin of PHE is the peculiar
time-reversal-breaking effect of an in-plane magnetic field, which
anisotropically lifts the protection of surface Dirac fermions from
back-scattering. The key signature of the field-induced anisotropy is a strong
dependence on the gate voltage with a characteristic two-peak structure near
the Dirac point which is explained theoretically using a self-consistent
T-matrix approximation. The observed PHE provides a new tool to analyze and
manipulate the topological protection of the TI surface in future experiments.
