  We propose a way of measuring the photon polarization in radiative B decays
into K resonance states decaying to K\pi\pi, which can test the Standard Model
and probe new physics. The photon polarization is shown to be measured by the
up-down asymmetry of the photon direction relative to the K\pi\pi decay plane
in the K resonance rest frame. The integrated asymmetry in K_1(1400)\to
K\pi\pi, calculated to be 0.34\pm 0.05 in the Standard Model, is measurable at
currently operating B factories.
