Polarization observations of the cosmic microwave background with the Cosmic Background Imager from September 2002 to May 2004 provide a significant detection of the E-mode polarization and reveal an angular power spectrum of polarized emission showing peaks and valleys that are shifted in phase by half a cycle relative to those of the total intensity spectrum. This key agreement between the phase of the observed polarization spectrum and that predicted on the basis of the total intensity spectrum provides support for the standard model of cosmology, in which dark matter and dark energy are the dominant constituents, the geometry is close to flat, and primordial density fluctuations are predominantly adiabatic with a matter power spectrum commensurate with inflationary cosmological models.