If life exists beneath the Martian surface similar to terrestrial bacteria that rely upon chemical reactions involving H2 and/or CO as energy sources, then it may be possible to infer its existence by observing metabolic by-products that would appear as trace gases in the Martian atmosphere. We have studied the fate of organic trace gases in the Martian atmosphere and find that most have very short chemical lifetimes, however CH4 has a chemical lifetime of about 300 yrs and thus it will tend to be uniformly distributed in the Martian atmosphere. Using the current observational upper limit on atmospheric CH4 we deduce that its flux, from all sources, into the Martian atmosphere must be at least 105 times less than terrestrial value. If there are abiotic sources of CH4 on Mars then the biological component of the CH4 must be even less.