Investigations of interacting and merging galaxies at high redshift are vital to our understanding of their formation and evolution. To date, the identification of interactions at z ~ 3 and above has relied on rest-frame ultraviolet morphological parameters. Here, we present five serendipitous spectroscopic z ~ 3 Lyman break galaxy (LBG) pairs with projected proper separations <15h-1kpc in our survey of nine separate deep Keck fields. The data consist of 140 of our highest signal-to-noise ratio LBG spectra and ~500 of our most confident colour-selected LBGs. We show that the pairs are composed of two distinct close and/or interacting LBGs from a detailed analysis of the rest-frame ultraviolet 1D and 2D spectra and the deep broad-band images. In addition, we show that the number and separation distribution of the pairs is expected from (1) the two-point angular correlation function when applied to the LBG pair separation distribution in our survey and ~2500 colour-selected LBGs from the literature and (2) an analysis of a carefully matched high-resolution hybrid numerical and analytical cosmological simulation. Because the spectroscopic slitlets have random orientations with respect to the close pairs on the sky, the serendipitous pairs provide an unbiased sampling of the underlying close pair fraction. Finally, we discover two Lyα emitters (LAEs) in our slitlets and find that they reside within 50 projected h-1kpc of the spectroscopic LBGs. In this work, we uncover a strong relationship between Lyα emission and pair separation. All confirmed and all candidate LBG pairs with separations of <=15 projected h-1kpc exhibit Lyα in emission and we find an indication of an overabundance of Lyα emission in pairs with <=50 projected h-1kpc separations. This relationship suggests a picture in which a measurable fraction of the Lyα emission of LBGs, and potentially LAEs, is generated via interaction mechanisms such as triggered star formation and the dispersal of obscuring gas and dust. As a result, serendipitous spectroscopic close pairs provide a unique means to help identify and study high-redshift galaxy interactions using ground-based optical data.