  We analyse \textit{ROSAT} and \textit{Chandra} ACIS X-ray observations and HI
absorption spectra of the
  $\gamma$ Cygni supernova remnant (G78.2+2.1, DR4). The \textit{ROSAT}
All-Sky-Survey image shows G78.2+2.1 has an adjacent limb-brightened shell
north of it. A new \textit{ROSAT} mosaic shows details of the X-ray emission
over the entire face of G78.2+2.1. We also create \textit{Chandra} mosaics
which cover much of the northern rim and central regions of G78.2+2.1. HI
absorption spectra result in association of G78.2+2.1 with the $\gamma$ Cygni
nebula, with distance 1.7 to 2.6 kpc. Chandra spectra for G78.2+2.1 give an
X-ray temperature of 0.6-1.2 keV (90% error), and that a Sedov model has age of
6800-10000 yr. A compact power-law X-ray source in G78.2+2.1 is consistent with
the same distance as G78.2+2.1. The northern X-ray shell is identified with a
B3 star at distance of 980 pc and is proposed as a stellar wind bubble.
