We compute the contributions to large-p(T) J/psi production at HERA co
ming from fragmentation of gluons and charm quarks. We find that the c
harm quark fragmentation contribution dominates over the direct produc
tion of J/psi via photon-gluon fusion at large-p(T), while the gluon f
ragmentation is negligibly small over the whole range of p(T). An expe
rimental study of p(T) distributions of J/psi at HERA will provide a d
irect probe of the charm quark fragmentation functions.