  We have conducted a VLA search for radio pulsars at the positions of 44
nearby OB runaway stars. The observations involved both searching images for
point sources of continuum emission and a time series analysis. Our mean flux
sensitivity to pulsars slower than 50 ms was 0.2 mJy. No new pulsars were found
in the survey. The size of the survey, combined with the high sensitivity of
the observations, sets a significant constraint on the probability, $f_p$, of a
runaway OB star having an observable pulsar companion. We find $f_p \le 6.5$\%
with 95\% confidence, if the general pulsar luminosity function is applicable
to OB star pulsar companions. If a pulsar beaming fraction of \onethird\ is
assumed, then we estimate that fewer than 20\% of runaway OB stars have neutron
star companions, unless pulsed radio emission is frequently obscured by the OB
stellar wind. Our result is consistent with the dynamical (or cluster) ejection
model for the formation of OB runaways. The supernova ejection model is not
ruled out, but is constrained by these observations to allow only a small
binary survival fraction, which may be accommodated if neutron stars acquire
significant natal kicks. According to Leonard, Hills and Dewey (1994), a 20\%
survival fraction corresponds to a 3-d kick velocity of 420 km s$^{-1}$. This
value is in close agreement with recent revisions of the pulsar velocity
distribution.
