  We present new sensitive wide-band measurements of the fine structure line
3^P_1 -> 3^P_0 (J=1-0, 492GHz) of neutral atomic carbon (CI) in the two typical
Ultra Luminous Infrared Galaxies NGC6240 and Arp220. We then use them along
with several other CI measurements in similar objects found in the literature
to estimate their global molecular gas content under the assumption of a full
CI-H_2 concomitance. We find excellent agreement between the H_2 gas mass
estimated with this method and the standard methods using 12^CO. This may
provide a new way to measure H_2 gas mass in galaxies, and one which may be
very valuable in ULIRGs since in such systems the bright 12^CO emission is
known to systematically overestimate the gas mass while their 13^CO emission is
usually very weak. At redshifts z>=1 the CI J=1-0 line shifts to much more
favorable atmospheric windows and can become a viable alternative tracer of the
H_2 gas fueling starburst events in the distant Universe.
