The production rate of prompt \(\psi'\)'s at large transverse momentum at the Tevatron is larger than theoretical expectations by about a factor of 30. As a solution to this puzzle, we suggest that the dominant \(\psi'\) production mechanism is the fragmentation of a gluon into a \(c \bar c\) pair in a pointlike color-octet S-wave state, which subsequently evolves nonperturbatively into a \(\psi'\) plus light hadrons. The contribution to the fragmentation function from this process is enhanced by a short-distance factor of \(1/\alpha_s^2\) relative to the conventional color-singlet contribution. This may compensate for the suppression by \(v^4\), where \(v\) is the relative momentum of the charm quark in the \(\psi'\). If this is indeed the dominant production mechanism at large \(p_T\), then the prompt \(\psi'\)'s that are observed at the Tevatron should almost always be associated with a jet of light hadrons.