It is possible to imagine technology capable of placing individual atoms of various kinds in precise locations in space to build molecules. If you had such a technology and a supply of carbon, oxygen, nitrogen, etc. you could assemble living things of any configuration. You would also have to provide some means of stabilizing the intermediate states of constituent molecules and structures that are inherently unstable. Transporters and replicators are supposed accomplish essentially this construction in the Star Trek (and other SciFi) series with the additional complication of assembling the matter from energy on-the-fly. With sufficient power and intelligence it is theoretically possible, but humans are far from creating the necessary inorganic machinery to build anything very sophisticated from constituent atoms.

Do you mean, is it possible to make an organism from abiotic or prebiotic (nonbiological) materials? It is not possible, at least so far as we know, to make any organism from only "inorganic" materials, because we cannot make a functioning organism without both hydrogen and carbon, the two elements which define "organic". Those two types of atoms have reactive properties which life as we know it depends on. If you do actually mean, is it possible to put together a string of DNA which will assemble an organism from abiotic, nonbiological molecules, then potentially yes, although we haven't yet. We regularly assemble artificial bacterial chromosomes (BACs) as a tool to investigate already-existing genetic sequences, and these are inserted into host cells from which the original chromosome(s) have been either partially or fully removed. One page about it is available here: http://www.ornl.gov/sci/techresources/meetings/bacpac/index.shtml. The minimum number of genes on which an organism can function has also been mapped (as have the genes), and in theory it is possible to spur self-assembly from these instructions -- the intention for the project was announced by Craig Venter in 1999, but he said he was holding off on it until he was given a go-ahead by ethicists, and to my knowledge that has not been done. Beyond that, however, how an *entirely* brand-new or artificial organism could come into existance in a lab is an area of great interest, and the idea has been modelled in several ways; experiments addressing one aspect of it at a time are constantly being done. A paper about the assembly of organisms is available here: http://www.sciencemag.org/cgi/content/summary/303/5660/963, and the associated website for the project is available here: http://www.ees.lanl.gov/protocells/. There are further papers and books about the bridge from living to nonliving matter available, as well, including http://mitpress.mit.edu/catalog/item/default.asp?ttype=6&tid=10719 and a full paper on some of the issues here: http://www.springerlink.com/media/ege9fmtyqk5vnt3h9j5m/contributions/w/3/0/3/w3033447742x3462.pdf . (The fact that we have not done it yet, but that we believe it to be possible with sufficient investigation and experimentation, are neither contradictory nor a matter of blind faith. That is how science tackles every problem.)