We carried out an ALMA survey of 15 confirmed or candidate low-mass (<0.2 M⊙) members of the TW Hya Association (TWA) with the goal of detecting molecular gas in the form of CO emission, as well as of providing constraints on continuum emission due to cold dust. Our targets have spectral types of M4-L0 and hence represent the extreme low end of the TWA’s mass function. Our ALMA survey has yielded detections of 1.3 mm continuum emission around 4 systems (TWA 30B, 32, 33, and 34), suggesting the presence of cold dust grains. All continuum sources are unresolved. TWA 34 further shows 12CO(2–1) emission whose velocity structure is indicative of Keplerian rotation. Among the sample of known ~7–10 Myr-old star/disk systems, TWA 34, which lies just ~50 pc from Earth, is the lowest mass star thus far identified as harboring cold molecular gas in an orbiting disk.