  We analyze the spectrum of an unusually-low mass white dwarf,
SDSSJ123410.37-022802.9 (0335-264-52000), found in our recent, white dwarf
catalog from the SDSS DR1 data release. Two independent, model atmosphere fits
result in an accurate determination of atmospheric and stellar parameters. The
more hands-on analysis yields $T_{\rm eff}$ =17,470$\pm$750 K and $\log g$ =
6.38$\pm$0.05. We argue that the object cannot be a main sequence A star, a
horizontal branch or subdwarf B star. Instead, it is interpreted as a very low
mass white dwarf with a core composed of helium, with mass
($\sim$0.18-0.19$M_\odot$), similar to that published previously for the
unusual companion to the millisecond pulsar J1012+5307. The star probably
remains in a binary, perhaps even with an undiscovered or dead pulsar
companion. However, the companion might be a more-ordinary star, provided Roche
lobe mass transfer began shortly after the now-visible component left the main
sequence. A second SDSS low mass white dwarf candidate is also analyzed, but
the spectrum for this fainter object is of poorer quality. The sample appears
to include additional, similar candidates, worthy of more accurate observation.
Correct identification of any additional white dwarfs of extremely low mass
requires careful observation and interpretation.
