A possible X-ray detection of the newly discovered binary millisecond
radio pulsar PSR J1012+5307 was obtained from an archival ROSAT observ
ation. The 80 +/- 24 photons detected correspond to a 0.1-2.4 keV lumi
nosity of approximate to 2.5 x 10(30) ergs s(-1) at the nominal disper
sion measure distance of 520 pc. This luminosity is a factor of 2 less
than that of PSR J0437-4715, a near twin of PSR J1012+5307 in its spi
n parameters and energetics, and the only millisecond pulsar from whic
h pulsed X-rays have definitely been detected. PSR J1012+5307 is also
within 6 degrees of the ''H I hole'' in Ursa Major, providing a new es
timate of the electron column density through this region, which confi
rms that the ionized column density is also low. The small neutral col
umn density to PSR J1012+5307; N-H < 7.5 x 10(19) cm(-2), will facilit
ate future soft X-ray study, which will help to discriminate between t
hermal and nonthermal origins of the X-ray emission in millisecond pul
sars.