Two Chandra observations of the R Aqr symbiotic binary system taken 3.3 years apart show dramatic changes in the X-ray morphology and spectral characteristics in the inner 500 AU of this system. The morphology of the soft X-ray emission has evolved from a nearly circular region centered on the binary system to an hourglass shape that indicates the formation of a new southwest jet. Synchrotron radiation from the new jet in contemporaneous VLA radio spectra implies the physical conditions in the early stages of jet development are different from those in the more extended outer thermal jets known to exist for decades in this system. The central binary source has two X-ray spectral components in each of the two epochs, a soft component and a highly absorbed hard component characterized by T ~ 10^8 K if fit with a thermal plasma model. The spectrum hardened considerably between 2000.7 and 2004.0, primarily due to increased flux above 5 keV, suggesting a change in the accretion activity of the white dwarf on a timescale of a few years or less. Point-source Fe K emission is detected at the position of the central binary system in both observations. While the earlier observation shows evidence of only a single emission peak near Fe K alpha at 6.4 keV, the later observation shows a more complex emission structure between 6 and 7 keV. Finally, we have discovered a modulation in the hard X-ray flux with a period of 1734 s at a 95% confidence level in the 2004 observation only. The modulation potentially arises from standing shocks in an accretion column and we have explored the possibility that the white dwarf in R Aqr is analogous to the magnetic white dwarfs in Intermediate Polar.