We show that pairs of widely separated interferometers are advantageous for measuring the Stokes parameter V of a stochastic background of gravitational waves. This parameter characterizes asymmetry of amplitudes of right- and left-handed waves, and generation of the asymmetry is closely related to parity violation in the early universe. The advantageous pairs include the kilometer-size interferometers LIGO (Livingston)-LCGT and AIGO-Virgo, which are relatively insensitive to Omega(GW) (the simple intensity of the background). Using at least three detectors, information of the intensity Omega(GW) and the degree of asymmetry V can be separately measured.