We present interferometric observations of CO ( 1–0 ) emission in the elliptical galaxy NGC 759 with an angular resolution of 3 . ^ { \prime \prime } 1 \times 2 . ^ { \prime \prime } 3 ( 990 \times 735 pc at a distance of 66 Mpc ) . NGC 759 contains 2.4 \times 10 ^ { 9 } { M } _ { \odot } of molecular gas . Most of the gas is confined to a small circumnuclear ring with a radius of 650 pc with an inclination of 40 ^ { \circ } . The maximum gas surface density in the ring is 750 { M } _ { \odot } \hbox { pc } ^ { -2 } . Although this value is very high , it is always less than or comparable to the critical gas surface density for large scale gravitational instabilities . The CO J =2 - 1/ J =1 - 0 line ratio is low ( 0.4 ) , implying sub-thermal excitation . This low ratio is consistent with a two–component molecular gas , consisting of a cold and dense phase , containing most of the mass , and a warm and diffuse gas component , dominating the CO emission . Compared to galaxies of similar gas surface densities , NGC 759 is underluminous in L _ { FIR } with respect to its molecular gas mass , suggesting that the star forming efficiency in NGC 759 is low . We discuss the possibility that the molecular gas and current star formation activity in NGC 759 could be signatures of a late stage of a merging between two gas–rich disk galaxies . We use a mass model of the underlying galaxy which is applicable to spherical galaxies with an r ^ { 1 / 4 } –luminosity profile when interpreting our CO data . This leads to more modest estimates of the molecular gas mass fraction and the surface gas density than would have been derived using simpler models , suggesting that many of the spectacular molecular gas properties of ultraluminous FIR galaxies , which could be described by similar mass distributions , may have to be revised .