  We report on the detection of two elongated X-ray features G359.89-0.08 and
G359.54+0.18 in the Galactic center (GC) region using the Chandra X-ray
Observatory. G359.89-0.08 is an elongated X-ray feature located $\sim$2\arcmin
in projection south of the center of the Galaxy, SgrA$^*$. This X-ray feature
source is partially coincident with a slightly curved (``wisp''-like)
non-thermal radio source. The X-ray spectrum of G359.89-0.08 can be best
characterized as non-thermal, with a photon index of 2. The morphological and
spectral characteristics of the X-ray and radio emission associated with
G359.89-0.08 are best interpreted as the synchrotron emission from a
ram-pressure confined pulsar wind nebula. G359.54+0.18 is one of the most
prominent radio non-thermal filaments (NTFs) in the GC region, located
$\sim$30\arcmin in projection from SgrA$^*$. A narrow ($\sim$10\arcsec)
filament of X-ray emission appears to arise from one of the two strands that
comprise the radio NTF. Although the photon statistics are poor for this
source, the X-ray emission is also likely to be non-thermal in nature. Several
models for the production of X-ray emission in G359.54+0.18 are discussed.
