  We report detections of three z ~ 2.5 submillimeter-selected galaxies (SMGs;
SMM J14011+0252, SMM J14009+0252, SMM J04431+0210) in the lowest rotational
transition of the carbon monoxide molecule (CO J = 1-0) and one nondetection
(SMM J04433+0210). For the three galaxies we detected, we find a
line-integrated brightness temperature ratio of the J = 3-2 and 1-0 lines of
0.68 +/- 0.08; the 1-0 line is stronger than predicted by the frequent
assumption of equal brightnesses in the two lines and by most single-component
models. The observed ratio suggests that mass estimates for SMGs based on J =
3-2 observations and J = 1-0 column density or mass conversion factors are low
by a factor of 1.5. Comparison of the 1-0 line intensities with intensities of
higher-J transitions indicates that single-component models for the
interstellar media in SMGs are incomplete. The small dispersion in the ratio,
along with published detections of CO lines with J_upper > 3 in most of the
sources, indicates that the emission is from multi-component interstellar media
with physical structures common to many classes of galaxies. This result tends
to rule out the lowest scaling factors between CO luminosity and molecular gas
mass, and further increases molecular mass estimates calibrated against
observations of galaxies in the local universe. We also describe and
demonstrate a statistically sound method for finding weak lines in broadband
spectra that will find application in searches for molecular lines from sources
at unknown redshifts.
