  Using archival Chandra data we studied the X-ray emission properties of PSR
B2224+65 and its environment. Albeit limited by photon statistics the spectral
analysis suggests that the bulk of the emission from PSR B2224+65 is
non-thermal. Fitting a power-law to the observed energy spectrum yields a
photon index of $\Gamma=1.58^{+0.43}_{-0.33}$. The possible origin of the
non-thermal pulsar emission is discussed in the context of the outer-gap model.
We did not find any evidence for a compact nebula around PSR B2224+65 though
the Chandra data reveal the existence of an extended feature which appears to
be associated with PSR B2224+65. It extends from the pulsar position about 2
arcmin to the north-west. Its orientation deviates by $\sim118^{\circ}$ from
the pulsar's proper motion direction. Investigating its energy spectrum shows
that the emission of this extended feature is much harder than that of the
pulsar itself and is non-thermal in nature.
