  Using precise full-sky observations from Planck, and applying several methods
of component separation, we identify and characterize the emission from the
Galactic "haze" at microwave wavelengths. The haze is a distinct component of
diffuse Galactic emission, roughly centered on the Galactic centre, and extends
to |b| ~35 deg in Galactic latitude and |l| ~15 deg in longitude. By combining
the Planck data with observations from the WMAP we are able to determine the
spectrum of this emission to high accuracy, unhindered by the large systematic
biases present in previous analyses. The derived spectrum is consistent with
power-law emission with a spectral index of -2.55 +/- 0.05, thus excluding
free-free emission as the source and instead favouring hard-spectrum
synchrotron radiation from an electron population with a spectrum (number
density per energy) dN/dE ~ E^-2.1. At Galactic latitudes |b|<30 deg, the
microwave haze morphology is consistent with that of the Fermi gamma-ray "haze"
or "bubbles," indicating that we have a multi-wavelength view of a distinct
component of our Galaxy. Given both the very hard spectrum and the extended
nature of the emission, it is highly unlikely that the haze electrons result
from supernova shocks in the Galactic disk. Instead, a new mechanism for
cosmic-ray acceleration in the centre of our Galaxy is implied.
