High-resolution spectroscopy of stars on the red giant branch (RGB) of the globular cluster M15 has revealed a large ~1 dex dispersion in the abundances of r-process elements, like Ba and Eu. Neutron star mergers (NSMs) have been proposed as a major source of the r-process. However, most NSM models predict a delay time longer than the timescale for cluster formation. One possibility is that a NSM polluted the surfaces of stars in M15 long after the cluster finished forming. In this case, the abundances of the polluting elements would decrease in the first dredge-up as stars turn on to the RGB. We present Keck/DEIMOS abundances of Ba in 66 stars along the entire RGB and the top of the main sequence. The Ba abundances have no trend with stellar luminosity (evolutionary phase). Therefore, the stars were born with the Ba they have today, and Ba did not originate in a source with a delay time longer than the timescale for cluster formation. In particular, if the source of Ba was a neutron star merger, it would have had a very short delay time. Alternatively, if Ba enrichment took place before the formation of the cluster, an inhomogeneity of a factor of 30 in Ba abundance needs to be able to persist over the length scale of the gas cloud that formed M15, which is unlikely.