We present high sensitivity 12CO and 13CO J=1!0 molecular line maps covering the full extent of the parsec scale Haro 6-10 Herbig-Haro (HH) flow. We report the discovery of a molecular CO outflow along the axis of parsec-scale HH flow. Previous molecular studies missed the identification of the outflow probably due to their smaller mapping area and the confusing spectral features present towards the object. Our detailed molecular line study of the full 1.6 pc extent of the optical flow shows evidence for both blueshifted and redshifted gas set in motion by Haro 6-10 activity. The molecular outflow is centered at Haro 6-10, with redshifted gas being clumpy and directed towards the northeast, while blueshifted gas is in the southwest direction. The molecular gas terminates well within the cloud, short of the most distant HH objects of the optical flow. Contamination from an unrelated cloud along the same line of sight prevents a thorough study of the blueshifted outflow lobe and the mass distribution at the lowest velocities in both lobes. The cloud core in which Haro 6-10 is embedded is filamentary and flattened in the east-west direction. The total cloud mass is calculated from 13CO J=1--0 to be ~ 200 M⊙. The lower limit of the mass associated with the outflow is ~0.25 M⊙.