The ability to trace stars to common progenitors by using chemical abundance patterns (i.e. chemical tagging) is an integral component of Galactic Archeology. Determining to what extent we are able to believe conatal stars are chemically identical is critical to the feasibility of this method. We present detailed chemical abundances of 37 comoving pairs. Many of these pairs were likely conatal stars. These stars were selected specifically to have similar stellar parameters in order to reduce the influence of systematic errors in the abundance analysis. We measure abundances for 24 elements including Li, C, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, Y, Zr, Ba, La, Nd, Eu. We find an increase in the dispersion in the metallicity difference between comoving pairs as a function of the increasing separation between the stars. The majority of stars with separations less than 106 AU have a metallicity spread of ~0.05 dex, whereas the stars with separations beyond 106 AU have a spread of ~0.1 dex. This has implications for our ability to perform strong chemical tagging in the solar neighborhood and perhaps beyond.