We present δ13C, δ15N, and δ34S measurements on archaeological human and animal bone collagen samples from a shell midden dating to the Neolithic ca. 4000–3500 cal BC, together with measurements on modern fish and shellfish. These data were used in conjunction with the Bayesian mixing model, Food Reconstruction Using Isotopic Transferred Signals (FRUITS), to reconstruct human diet at the site. We demonstrate the importance of using a geographically appropriate faunal baseline in stable isotope paleodietary studies, and suggest that Neolithic individuals at this site consumed up to ca. 21% of dietary protein from marine resources, despite stable isotope ratios that imply a wholly terrestrial diet. This marine resource consumption does not significantly shift the radiocarbon (14C) dates of these individuals, so although we must consider the use of marine resources at the site, the chronology that has previously been established is secure. The δ13C and δ15N measurements from the archaeological herbivore bone collagen indicate that it is unlikely they ate plants enriched with fertilisers such as manure or seaweed. The δ34S values reveal a sea-spray effect; therefore, in this instance, δ34S cannot be used as a dietary indicator but can be used to demonstrate the likely locality of the fauna.