  We argue that the anomalous power asymmetry observed in the cosmic microwave
background (CMB) may have originated in a cosmic bounce preceding inflation. In
loop quantum cosmology (LQC) the big bang singularity is generically replaced
by a bounce due to quantum gravitational effects. We compute the spectrum of
inflationary non-Gaussianity and show that strong correlation between
observable scales and modes with longer (super-horizon) wavelength arise as a
consequence of the evolution of perturbations across the LQC bounce. These
correlations are strongly scale dependent and induce a dipole-dominated
modulation on large angular scales in the CMB, in agreement with observations.
