  We analyze Chandra observations of the Wolf-Rayet (WR) bubble NGC 6888. This
WR bubble presents similar spectral and morphological X-ray characteristics to
those of S 308, the only other WR bubble also showing X-ray emission. The
observed spectrum is soft, peaking at the N VII line emission at 0.5 keV with
additional line emission at 0.7 - 0.9 keV and a weak tail of harder emission up
to ~1.5 keV. This spectrum can be described by a two-temperature optically thin
plasma emission model (T_{1}~1.4x10^{6} K, T_{2}~7.4x10^{6} K). We confirm the
results of previous X-ray observations that no noticeable temperature
variations are detected in the nebula. The X-ray-emitting plasma is distributed
in three apparent morphological components: two caps along the tips of the
major axis and an extra contribution toward the northwest blowout not reported
in previous analysis of the X-ray emission toward this WR nebula. Using the
plasma model fits of the Chandra ACIS spectra for the physical properties of
the hot gas and the ROSAT PSPC image to account for the incomplete coverage of
Chandra observations, we estimate a luminosity of L_X = (7.7\pm0.1)x10^{33}
erg/s for NGC 6888 at a distance of 1.26 kpc. The average rms electron density
of the X-ray-emitting gas is >= 0.4 cm^{-3} for a total mass >= 1.2 Msun.
