  We derive constraints that must be satisfied by the sources of ~10^{15} to
~10^{18} eV cosmic rays, under the assumption that the sources are Galactic. We
show that while these constraints are not satisfied by ordinary supernovae
(SNe), which are believed to be the sources of <10^{15} eV cosmic rays, they
may be satisfied by the recently discovered class of trans-relativistic
supernovae (TRSNe), which were observed in association with gamma-ray bursts.
We define TRSNe as SNe that deposit a large fraction, f_R>10^{-2}, of their
kinetic energy in mildly relativistic, \gamma\beta>1, ejecta. The high velocity
ejecta enable particle acceleration to ~10^{18} eV, and the large value of f_R
(compared to f_R~10^{-7} for ordinary SNe) ensures that if TRSNe produce the
observed ~10^{18} eV cosmic ray flux, they do not overproduce the flux at lower
energies. This, combined with the estimated rate and energy production of
TRSNe, imply that Galactic TRSNe may be the sources of cosmic rays with
energies up to ~10^{18}eV .
