We predict the rate at which gamma-ray burst (GRB) afterglows should be det
ected in supernova (SN) searches as a function of limiting flux. Although G
RB afterglows are rarer than supernovae (SNs), they are detectable at great
er distances because of their higher intrinsic luminosity. Assuming that GR
Bs trace the cosmic star formation history and that every GRB gives rise to
a bright afterglow, we find that the average detection rate of SNs and aft
erglows should be comparable at limiting magnitudes brighter than K = 18. T
he actual rate of afterglows is expected to be somewhat lower since only a
fraction of all gamma-ray-selected GRBs were observed to have associated af
terglows. Hence, current and future SN searches can place strong constraint
s on the afterglow appearance fraction of GRB sources.