We report detections of three z \sim 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 \pm 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 .