We address theoretically and numerically the possibility of observing ellipticity in high-order harmonic generation (HHG) from aligned molecules driven by linearly polarized fields—a subject of controversy in the recent literature with significant implications. To that end we develop a numerical method for solution of the electronic dynamics and extend a recently developed theory of HHG from aligned molecules. Our numerical results are in good agreement with recent experimental data. The theory explains analytically several observations of polarization experiments. We note the conditions under which ellipticity can be observed and the information content of elliptically polarized harmonics regarding the molecular system.