  We present the results of a search for molecular gas emission via the CO line
in the far outer disk of the nearby spiral, NGC 6946. The positions targeted
were chosen to lie on or near previously-identified outer disk HII regions.
Molecular gas was clearly detected out to 1.3 R$_{25}$, with a further
tentative detection at 1.4 R$_{25}$. The CO detections show excellent agreement
with the HI velocities and imply beam-averaged column densities of $0.3-9\times
10^{20}$ cm$^{-2}$ and molecular gas masses of (2-70)$\times 10^{5}$ M$_{\sun}$
per 21$''$ beam (560pc). We find evidence for an abrupt decrease in the
molecular fraction at the edge of the optical disk, similar to that seen
previously in the azimuthally-averaged areal star formation rate. Our
observations provide new constraints on the factors that determine the presence
and detectability of molecular gas in the outskirts of galaxies, and suggest
that neither the HI column, the metallicity or the local heating rate alone
plays a dominant role.
