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 < \ell < 2100 and is based on observations of an effective sky area of 25 \deg ^ { 2 } with 3.5′ 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 97.2 % 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 \pm 0.61 ( { stat } ) ^ { +0.04 } _ { -0.12 } ( { sys } ) \pm 0.07 ( { multi } ) , where A _ { BB } = 1 is the fiducial wmap -9 \Lambda CDM 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 } .