Archaic admixture has had a substantial impact on human evolution with multiple events across different clades, including from extinct hominins such as Neanderthals and Denisovans into modern humans. In great apes, archaic admixture has been identified in chimpanzees and bonobos but the possibility of such events has not been explored in other species. Here, we address this question using high-coverage whole-genome sequences from all four extant gorilla subspecies, including six newly sequenced eastern gorillas from previously unsampled geographic regions. Using approximate Bayesian computation with neural networks to model the demographic history of gorillas, we find a signature of admixture from an archaic 'ghost' lineage into the common ancestor of eastern gorillas but not western gorillas. We infer that up to 3% of the genome of these individuals is introgressed from an archaic lineage that diverged more than 3 million years ago from the common ancestor of all extant gorillas. This introgression event took place before the split of mountain and eastern lowland gorillas, probably more than 40 thousand years ago and may have influenced perception of bitter taste in eastern gorillas. When comparing the introgression landscapes of gorillas, humans and bonobos, we find a consistent depletion of introgressed fragments on the X chromosome across these species. However, depletion in protein-coding content is not detectable in eastern gorillas, possibly as a consequence of stronger genetic drift in this species.