With 40 ks of Chandra ACIS-S3 exposure, new information on both the starburst and QSO components of the X-ray emission of Markarian 231, an ultraluminous infrared galaxy and broad absorption line QSO, has been obtained. The bulk of the X-ray luminosity is emitted from an unresolved nuclear point source, and the spectrum is remarkably hard, with the majority of the flux emitted above 2 keV. Most notably, significant nuclear variability (a decrease of $45% in approximately 6 hr) at energies above 2 keV indicates that Chandra has probed within light-hours of the central black hole. Although we concur with Maloney & Reynolds that the direct continuum is not observed, this variability coupled with the 188 eV upper limit on the equivalent width of the Fe K emission line argues against the reflection-dominated model put forth by these authors based on their ASCA data. Instead, we favor a model in which a small, Compton-thick absorber blocks the direct X-rays, and only indirect, scattered X-rays from multiple lines of sight can reach the observer. Extended soft, thermal emission encompasses the optical extent of the galaxy and exhibits resolved structure. An off-nuclear X-ray source with a 0.35-8.0 keV luminosity of L X ¼ 7 Â 10 39 ergs s À1 , consistent with the ultraluminous X-ray sources in other nearby starbursts, is detected. We also present an unpublished Faint Object Spectrograph spectrum from the Hubble Space Telescope archive showing the broad C iv absorption.