We present an analysis of the Chandra Advanced CCD Imaging Spectrometer ( ACIS ) observation of the intracluster gas associated with the cluster of galaxies surrounding Cygnus A . The dominant gaseous structure is a roughly elliptical ( presumably prolate spheroidal in three dimensions ) feature with semi-major axis \simeq 1. ^ { \prime } 1 ( \simeq 100 kpc ) . This structure apparently represents intracluster gas which has been swept up and compressed by a cavity inflated in this gas by relativistic material which has passed through the ends of the radio jets . The X-ray emitting gas shows this prolate spheroidal morphology to \simeq 1. ^ { \prime } 2 ( 110 kpc ) from the radio galaxy , but is spherical on larger scales . The X-ray emission from the intracluster gas extends to at least 8 ^ { \prime } ( \simeq 720 kpc ) from the radio galaxy , and a second , extended source of X-ray emission ( probably associated with a second cluster of galaxies ) is seen some 12 ^ { \prime } ( \simeq 1 Mpc ) to the NW of Cygnus A . The X-ray spectrum of the integrated intracluster gas imaged on the S3 chip ( dimensions 8 ^ { \prime } \times 8 ^ { \prime } = 720 \times 720 kpc ) , excluding the contribution from the radio galaxy and other compact sources of X-ray emission , has a gas temperature , metallicity , and unabsorbed 2–10 keV rest-frame luminosity of 7.7 keV , 0.34 times solar , and 3.5 \times 10 ^ { 44 } erg s ^ { -1 } , respectively . We have deprojected the X-ray spectra taken from 12 elliptical and circular annuli in order to derive a run of temperature , metallicity , density , and pressure as a function of radius . The temperature of the X-ray emitting gas drops from \simeq 8 keV more than 100 kpc from the center to \simeq 5 keV some 80 kpc from the center , with the coolest gas immediately adjacent to the radio galaxy . “ Belts ” of slightly cooler ( \simeq 4 keV ) X-ray emitting gas run around the minor dimension of the cavity created by the radio source , while the limb-brightened edges of the cavity are slightly hotter ( \simeq 6 keV ) , perhaps as a result of heating by a bow shock driven by the probably expanding cavity into the intracluster gas . There is a metallicity gradient in the X-ray emitting gas , with the highest metallicities ( \sim solar ) found close to the center , decreasing to \sim 0.3 solar in the outer parts . We have used the assumption of hydrostatic equilibrium to derive a total cluster mass within 500 kpc of 2.0 \times 10 ^ { 14 } M _ { \odot } and 2.8 \times 10 ^ { 14 } M _ { \odot } for a constant and centrally decreasing temperature profile , respectively . The total mass of X-ray emitting gas within the same radius is 1.1 \times 10 ^ { 13 } M _ { \odot } . Thus , the gas fraction of the cluster within 500 kpc is 0.055 and 0.039 for the constant and centrally decreasing temperature profiles , respectively .