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 ^ { \prime \prime } 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 .