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 isotropic SGWB. We present the first upper limit on this parity violation from direct gravitational-wave measurements by measuring polarization of the SGWB in recent LIGO data and by assuming a generic power-law SGWB spectrum across the LIGO-sensitive frequency region. We also estimate sensitivity to parity violation for future generations of gravitational-wave detectors, both for a power-law spectrum and for a specific model of axion inflation. Since astrophysical sources are not expected to produce a polarized SGWB, measurements of polarization in the SGWB would provide a new way of differentiating between the cosmological and astrophysical SGWB sources. © 2013 Elsevier B.V.