Depends on your personal tolerance for the complexity indicated by the word "chemical". The presence of "deoxyribonucleic acid" on its own does not prove life, as that term covers simple cases of it that could conceivably naturally occur. However, if you've got a multi-million base pair chain of the stuff, wrapped up in chromatin, and bespeckled with all manner of useful-looking biochemical doohickeys attached to it, I'm willing to say that's definitely indicative of life. Is that a "chemical"? I'd certainly call that a "molecule" that could only be produced by life.
In principle or practice? There a large number of secondary product compounds produced by microorganisms that have never been synthetically synthesised, but in theory they all could be.
If you want to prove that an organic compound has come from a living system you look for carbon isotope enrichment or depletion - more C12 and less C13 than found in the environment.
I've read that this question can be answered by looking at the chirality of the chemical(s) in question. If the levorotatory and dextrorotatory isomers are unevenly distributed, that's a hint that the substance originated in biological processes.
Not sure if that's still the current thinking, or if it ever was, but I found it interesting when I ran across it.