We present a sample of 407 z~3 Lyman break galaxies (LBGs) to a limiting isophotal u-band magnitude of 27.6mag in the Hubble Ultra Deep Field. The LBGs are selected using a combination of photometric redshifts and the u-band drop-out technique enabled by the introduction of an extremely deep u-band image obtained with the Keck I telescope and the blue channel of the Low Resolution Imaging Spectrometer. The Keck u-band image, totaling 9hr of integration time, has a 1{sigma} depth of 30.7mag/arcsec^2^, making it one of the most sensitive u-band images ever obtained. The u-band image also substantially improves the accuracy of photometric redshift measurements of ~50% of the z~3 LBGs, significantly reducing the traditional degeneracy of colors between z~3 and z~0.2 galaxies.