  We report on the results of Chandra X-ray observations of the $\gamma$-ray
radio-quiet pulsar J1932+1916. We confirm the previous detection of the pulsar
counterpart and its pulsar wind nebula in X-rays from low spatial resolution
data obtained by Suzaku and Swift. The Chandra data with much better spatial
resolution resolved the fine structure of the nebula in the pulsar vicinity,
which can be interpreted as jets bent by the ram pressure. The size of this
compact part is about 30'', and it is surrounded by a weak asymmetric diffusive
emission extended up to $\approx$ 2.8'. The X-ray spectra of the pulsar, the
compact and extended parts of the nebula can be described by the power-law
models with photon indexes of 0.44, 2.34 and 2.14, respectively. The actual
pulsar's X-ray flux is several times weaker than it was obtained with Suzaku
and Swift where it was dominated by the unresolved nebula. We discuss possible
associations of J1932+1916 with the nearby supernova remnant G54.4-0.3.
