  The diffractive production of vector bosons at the Tevatron is studied. We
take a hard pomeron flux and use the H1 parton density functions extracted from
their measurement of F_2^{D(3)}. To this we add a reggeon exchange
contribution. We find that the ratio of diffractive to non-diffractive W boson
production is in good agreement with the CDF data. We note that the poorly
understood reggeon contribution might be as large as the pomeron contribution
in the kinematic range of the data. We also note that our pomeron exchange
contribution is much smaller than earlier predictions due to our use of a hard
pomeron flux. All our results have been obtained using the lowest order matrix
elements and we have compared to the results obtained using a modified version
of Herwig which is capable of generating a wide variety of diffractive
scattering processes. Gap survival is estimated using Pythia and is found to be
around 60%. We make predictions which could be compared to future measurements
of diffractive Drell-Yan production.
