Argon is an extremely chemically inert element. HArF is presently the only experimentally known neutral molecule containing a chemically bound argon atom. Ab initio calculations at the MP2 and CCSD(T) levels presented here suggest, however, the existence of whole families of additional molecules. Explicitly predicted are FArCCH, with an argon-carbon bond, and FArSiF3, with an argon-silicon bond. These metastable compounds are found to be protected from decomposition by relatively high energy barriers. Other organo-argon and organo-silicon molecules derived from the above should be equally stable. The results may open the way to a substantial field of "argon chemistry." (C) 2003 American Institute of Physics.