  We report the detection of 15 GHz radio continuum emission associated with
the classical Cepheid variable star delta Cephei based on observations with the
Karl G. Jansky Very Large Array. Our results constitute the first probable
detection of radio continuum emission from a classical Cepheid. We observed the
star at pulsation phase phi~0.43 (corresponding to the phase of maximum radius
and minimum temperature) during three pulsation cycles in late 2018 and
detected statistically significant emission (>5 sigma) during one of the three
epochs. The observed radio emission appears to be variable at a >~10% level on
timescales of days to weeks. We also present an upper limit on the 10 GHz flux
density at pulsation phase phi=0.31 from an observation in 2014. We discuss
possible mechanisms that may produce the observed 15 GHz emission, but cannot
make a conclusive identification from the present data. The emission does not
appear to be consistent with originating from a close-in, late-type dwarf
companion, although this scenario cannot yet be strictly excluded. Previous
X-ray observations have shown that delta Cephei undergoes periodic increases in
X-ray flux during pulsation phase phi~0.43. The lack of radio detection in two
out of three observing epochs at phi~0.43 suggests that either the radio
emission is not linked with a particular pulsation phase, or else that the
strength of the generated radio emission in each pulsation cycle is variable.
