PSR J1809-1917 is a young ($tau=51$ kyr) energetic ($dot{E}=1.8times10^{36}$ erg s$^{-1}$) radio pulsar powering a pulsar wind nebula (PWN). We report on the results of three Chandra X-ray Observatory observations which show that the PWN consists of a small ($sim 20$) bright compact nebula (CN) and faint extended emission seen up to $2$ from the pulsar. The CN is elongated in the northeast-southwest direction and exhibits morphological and flux variability on a timescale of a few months. We also find evidence of small arcsecond-scale jets extending from the pulsar along the same direction, and exhibiting a hard power-law (PL) spectrum with photon index $Gamma_{rm jet}=1.2pm0.1$. The more extended emission and CN share the same symmetry axis, which is also aligned with the direction toward the TeV $gamma$-ray source HESS J1809--193, supporting their association. The spectrum of the extended nebula (EN) fits an absorbed PL with about the same slope as that of the CN, $Gamma_{rm CN}approxGamma_{rm EN}=1.55pm0.09$; no spectral changes across the ENs 2 pc extent are seen. The total PWN 0.5-8 keV luminosity is $L_{rm PWN}approx 9times10^{32}$ erg s$^{-1}$, about half of which is due to the EN.
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