  We report a measurement of the B-mode polarization power spectrum in the
cosmic microwave background (CMB) using the POLARBEAR experiment in Chile. The
faint B-mode polarization signature carries information about the Universe's
entire history of gravitational structure formation, and the cosmic inflation
that may have occurred in the very early Universe. Our measurement covers the
angular multipole range 500 < l < 2100 and is based on observations of an
effective sky area of 25 square degrees with 3.5 arcmin resolution at 150 GHz.
On these angular scales, gravitational lensing of the CMB by intervening
structure in the Universe is expected to be the dominant source of B-mode
polarization. Including both systematic and statistical uncertainties, the
hypothesis of no B-mode polarization power from gravitational lensing is
rejected at 97.1% confidence. The band powers are consistent with the standard
cosmological model. Fitting a single lensing amplitude parameter A_BB to the
measured band powers, A_BB = 1.12 +/- 0.61 (stat) +0.04/-0.12 (sys) +/- 0.07
(multi), where A_BB = 1 is the fiducial WMAP-9 LCDM value. In this expression,
"stat" refers to the statistical uncertainty, "sys" to the systematic
uncertainty associated with possible biases from the instrument and
astrophysical foregrounds, and "multi" to the calibration uncertainties that
have a multiplicative effect on the measured amplitude A_BB.
