Recent progress in our searches for complex interstellar molecules, which may be important for the origin of life on habitable planets, is reviewed. The molecular abundance ranges and current search limits observed in a number of "hot core" sources are tabulated and discussed. The abundance limits reached in searches for most complex interstellar molecules are not much lower than the detection levels of other large molecules. While our detection of c-C_2H_4O (ethylene oxide, oxirane) may suggest the interstellar presence of the next larger similar ring C-C_4H_4O (furan - the core of the simple sugars ribose and deoxyri-bose, which form the backbones of RNA and DNA), our current search limits are just barely lower than the abundance level of ethylene oxide. Really deep searches for prebiotic molecules in compact cloud cores will have to await the erection of the very sensitive aperture synthesis instrument ALMA, the Atacama Large Millimetre Array, to be located in the Chilean Andes.
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