The present study examined the hypothesis that left hemisphere (LH) equivalent language capabilities in the right hemisphere (RH) are inhibited in neurologically intact individuals by testing healthy young right-handers with a history of familial sinistrality (FS+, i.e. with at least one left handed biological relative), a population documented to show greater variability for RH language processing. Event-Related Potential (ERP) and split visual field presentation techniques were combined to assess LH- and RH- biased responses to syntactic category violations. In addition, a bilateral flanker task was used to measure inter-hemispheric inhibition ability in the same set of participants. Replicating prior findings, in addition to the LH-biased P600 grammaticality effect previously seen for right-handers in general, a fair amount, though not all, of FS + right-handers showed RH-biased P600 responses, leading to a reliable RH P600 grammaticality effect at the group level. Capitalizing on the variability of RH P600 responses, our results further revealed that reduced RH-biased P600 effects were reliably correlated with more effective RH inhibition (indexed by smaller reaction time differences between incongruent and neutral flankers presented to the RH via the left visual field). These results corroborated previous findings that the RH is capable of processing syntactic information in a manner qualitatively similar to that in the LH and further demonstrated that LH-equivalent processing in the RH as indexed by the P600 responses is modulated by RH inhibition, contributing to inter-individual variability in syntactic lateralization.