  A linear modulation of the primordial perturbations is proposed as an
explanation for the observed asymmetry between the northern and southern
hemispheres of the Wilkinson Microwave Anisotropy Probe (WMAP) data. A cut sky,
reduced resolution third year "Internal Linear Combination" (ILC) map was used
to estimate the modulation parameters. A foreground template and a modulated
plus unmodulated monopole and dipole were projected out of the likelihood. The
effective chi squared is reduced by nine for three extra parameters. The mean
Galactic colatitude and longitude, of the modulation, with 68%, 95% and 99.7%
confidence intervals were 56^{+17 +36 +65}_{-17 -35 -51} and 63^{+28 +59
+105}_{-26 -58 -213}. The mean percentage change of the variance, across the
pole's of the modulation, was 62^{+18 +35 +57}_{-18 -35 -47}. Implications of
these results and possible generating mechanisms are discussed.
