  The process $e^+e^- \to q \bar q \gamma$ contains radiation zeros, i.e.
configurations of the four-momenta for which the scattering amplitude vanishes.
We calculate the positions of these zeros for $u$--quark and $d$--quark
production and assess the feasibility of identifying the zeros in experiments
at high energies. The radiation zeros are shown to occur also for massive
quarks, and we discuss how the $b \bar b \gamma$ final state may offer a
particularly clean environment in which to observe them.
