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We present morphological and kinematic evidence that the HH34 protostellar outflow extends symmetrically about the HH34 source for roughly 1.5 parsecs, and has a total length of at least 3 parsecs. The northern components of the flow (HH34N, HH126, HH85, HH33, and HH40) are all redshifted, while the southern components (HH34, HH34X, HH173, HH86, HH87, and HH88) are all blueshifted. The northern and southern components are symmetrically placed relative to the driving source HH34 IRS, and their radial velocities are symmetric relative to the radial velocity of the cloud core containing HH34 IRS. The magnitude of the radial velocity tends to decrease with increasing distance from HH34 IRS. Proper motions of some of the components (HH33, HH4O, HH85A, HH86A, HH86B, HH87, and HH88) were also determined and are consistent with the single flow hypothesis; the proper motions of knots north of the HH34 source are directed to the northwest, while those to the south are directed to the southeast. The proper motions also tend to decrease with increasing distance from the HH34 source. The dynamic age of the flow is at least 10<SUP>4</SUP> years. We propose that the parsec-scale chain of Herbig-Haro objects in the HH34 system is powered by a time variable, quasi-episodic jet and discuss the expected behavior of the resulting shock structures over the lifetime of the flow.