  We present the results of HI line and radio continuum observations of five
nearby E+A galaxies. These galaxies have spectra that are dominated by a young
stellar component but lack the emission lines characteristic of significant,
on-going star formation. They are selected from a unique sample of 21 E+A's
identified by Zabludoff et al.(1996) in their spectroscopic search for E+A
galaxies using the Las Campanas Redshift Survey, where over 11,000 nearby
galaxies were examined. The five E+A galaxies span a range of environments:
three are in the field and two are in clusters. Only one system was detected in
HI emission, the field E+A galaxy EA1, with a total flux of 0.30 +/- 0.02 Jy
km/s and an HI mass of (3.5 +/- 0.2) 10^9 h^(-2) M_sun. The HI morphology and
kinematics of EA 1 suggest a galaxy-galaxy interaction, with a dynamical age of
about 6 x 10^8 h^(-1) yr inferred from the HI tail lengths and velocities. This
age estimate is consistent with the interpretation drawn from optical
spectroscopy that starbursts in E+A galaxies began (and subsequently ended)
within the last 10^9 yr. Our HI detection limits are such that if the other
E+A's in our sample had the HI properties of EA 1, we would have detected (or
marginally detected) them. We conclude that E+A galaxies have a range of HI
properties. None of the galaxies were detected in radio continuum emission,
with upper limits to the radio power of about 10^21 h^(-2) W/Hz. Our limits
exclude the possibility that these E+A's are dust-enshrouded massive starburst
galaxies, but are insufficient to exclude modest star formation rates of less
than a few h^(-2) M_sun per yr.
