We raise the question of whether velocities of left and right circular
ly-polarized photons might be different (for reasons other than the we
ll-known Faraday effect). Such a difference could manifest itself eith
er in the time profiles of pulsed or bursting astronomical sources or
in the rotation of the direction of polarization of linearly polarized
radiation from them. The existing observations of pulsars, gamma ray
bursters, and quasar jets are used to set limits to the difference in
speed, \c(L) - c(R)\/(c) over bar between 10(-17) and 10(-32).