  We report Chandra ACIS and quasi-simultaneous RXTE observations of the
nearby, powerful radio galaxy Cygnus A, with the present paper focusing on the
properties of the active nucleus. In the Chandra observation, the hard (> a few
keV) X-ray emission is spatially unresolved with a size \approxlt 1 arcsec (1.5
kpc, H_0 = 50 km s^-1 Mpc^-1) and coincides with the radio and near infrared
nuclei. In contrast, the soft (< 2 keV) emission exhibits a bi-polar nebulosity
that aligns with the optical bi-polar continuum and emission-line structures
and approximately with the radio jet. In particular, the soft X-ray emission
corresponds very well with the [O III] \lambda 5007 and H\alpha + [N II]
\lambda\lambda 6548, 6583 nebulosity imaged with HST. At the location of the
nucleus there is only weak soft X-ray emission, an effect that may be intrinsic
or result from a dust lane that crosses the nucleus perpendicular to the source
axis. The spectra of the various X-ray components have been obtained by
simultaneous fits to the 6 detectors. The compact nucleus is detected to 100
keV and is well described by a heavily absorbed power law spectrum with
\Gamma_h = 1.52^{+0.12}_{-0.12} (similar to other narrow line radio galaxies)
and equivalent hydrogen column N_H (nuc) = 2.0^{+0.1}_{-0.2} \times 10^{23}
cm^-2.
  (Abstract truncated).
