  We report the observation of a novel nonlinear optical response from the
prototypical three-dimensional topological insulator Bi$_2$Se$_3$ through the
process of high-order harmonic generation. We find that the generation
efficiency increases as the laser polarization is changed from linear to
elliptical, and it becomes maximum for circular polarization. With the aid of a
microscopic theory and a detailed analysis of the measured spectra, we reveal
that such anomalous enhancement encodes the characteristic topology of the band
structure that originates from the interplay of strong spin-orbit coupling and
time-reversal symmetry protection. Our study reveals a new platform for chiral
strong-field physics and presents a novel, contact-free, all-optical approach
for the spectroscopy of topological insulators. The implications are in
ultrafast probing of topological phase transitions, light-field driven
dissipationless electronics, and quantum computation.
