We produce oriented rotational wave packets in CO and measure their characteristics via high harmonic generation. The wave packet is created using an intense, femtosecond laser pulse and its second harmonic. A delayed 800 nm pulse probes the wave packet, generating even-order high harmonics that arise from the broken symmetry induced by the orientation dynamics. The even-order harmonic radiation that we measure appears on a zero background, enabling us to accurately follow the temporal evolution of the wave packet. Our measurements reveal that, for the conditions optimum for harmonic generation, the orientation is produced by preferential ionization which depletes the sample of molecules of one orientation.