We have obtained a deep 670 ks CXO ACIS image of the remarkable pulsar wind nebula (PWN) of PSR J1709-4429, in 4 epochs during 2018-2019. Comparison with an archival 2004 data set provides a pulsar proper motion mu = 13 pm 3 mas/yr at a PA of 86 pm 9 degree (1 sigma combined statistical and systematic uncertainties), precluding birth near the center of SNR G343.1-2.3. At the pulsars characteristic age of 17 kyr, the association can be preserved through a combination of progenitor wind, birth kick and PWN outflow. Associated TeV emission may, however, indicate explosion in an earlier supernova. Inter-epoch comparison of the X-ray images shows that the PWN is dynamic, but we are unable to conclusively measure flow speeds from blob motion. The pulsar has generated a radio/X-ray wind bubble, and we argue that the PWNs long narrow jets are swept back by shocked pulsar wind venting from this cavity. These jets may trace the polar magnetic field lines of the PWN flow, an interesting challenge for numerical modeling.
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