  Fu and Kane have discovered that a topological insulator with induced s-wave
superconductivity (gap $\Delta_0$, Fermi velocity $v_{\rm F}$, Fermi energy
$\mu$) supports chiral Majorana modes propagating on the surface along the edge
with a magnetic insulator. We show that the direction of motion of the Majorana
fermions can be inverted by the counterflow of supercurrent, when the Cooper
pair momentum along the boundary exceeds $\Delta_0^2/\mu v_{\rm F}$. The
chirality inversion is signaled by a doubling of the thermal conductance of a
channel parallel to the supercurrent. Moreover, the inverted edge can transport
a nonzero electrical current, carried by a Dirac mode that appears when the
Majorana mode switches chirality. The chirality inversion is a unique signature
of Majorana fermions in a spinful topological superconductor: it does not exist
for spinless chiral p-wave pairing.
