  A stochastic gravitational-wave background (SGWB) is expected to arise from
the superposition of many independent and unresolved gravitational-wave
signals, of either cosmological or astrophysical origin. Some cosmological
models (characterized, for instance, by a pseudo-scalar inflaton, or by some
modification of gravity) break parity, leading to a polarized SGWB. We present
a new technique to measure this parity violation, which we then apply to the
recent results from LIGO to produce the first upper limit on parity violation
in the SGWB, assuming a generic power-law SGWB spectrum across the LIGO
sensitive frequency region. We also estimate sensitivity to parity violation of
the future generations of gravitational-wave detectors, both for a power-law
spectrum and for a model of axion inflation. This technique offers a new way of
differentiating between the cosmological and astrophysical sources of the
isotropic SGWB, as astrophysical sources are not expected to produce a
polarized SGWB.
