A short 30 minute ALMA observation of the early-type galaxy NGC 5044, which resides at the center of an X-ray bright group with a moderate cooling flow, has detected 24 molecular structures within the central 2.5 kpc. The masses of the molecular structures vary from 3e5 to 1e7 Mo3 and the CO(2-1) linewidths vary from 15 to 65 km/s. Given the large CO(2-1) linewidths, the observed structures are likely giant molecular associations (GMAs) and not individual molecular clouds (GMCs). Only a few of the GMAs are spatially resolved with the cycle 0 ALMA beam and the average density of these GMAs yields a GMC volume filling factor of about 15%. The observed masses of the resolved GMAs are insufficient for them to be gravitationally bound, however, the most massive GMA does contain a less massive component with a linewidth of 5.5 km/s (typical of an individual virialized GMC). We also show that the GMAs cannot be pressure confined by the hot gas. Given the observed CO(2-1) linewidths of the GMAs (i.e., the velocity dispersion of the embedded GMCs) they will likely disperse on a timescale of about 12 Myr, which is less than the central cooling time of the hot gas, so the embedded GMCs within a GMA must condense out of the hot gas at the same time and arise from local concentrations of thermally unstable parcels of hot gas. There are no indications of any disk-like molecular structures and all indications suggest that the molecular gas follows ballistic trajectories after condensing out of the thermally unstable hot gas. The 230 GHz luminosity of the central continuum source is 500 times greater than its low frequency radio luminosity and probably reflects a recent accretion event by the central supermassive black hole. The spectrum of the central continuum source also exhibits an absorption feature.