Recent research suggests that some people with aphasia preserve some ability to learn novel words and to retain them in the long-term. However, this novel word learning ability has been studied only in the context of single word-picture pairings. We examined the ability of people with chronic aphasia to learn novel words using a paradigm that presents new word forms together with a limited set of different possible visual referents and requires the identification of the correct word-object associations on the basis of online feedback. We also studied the relationship between word learning ability and aphasia severity, word processing abilities, and verbal short-term memory. We further examined the influence of gross lesion location on new word learning. The word learning task was first validated with a group of forty-five young adults. Fourteen participants with chronic aphasia were administered the task and underwent tests of immediate and long-term recognition memory at 1 week. Their performance was compared to that of a group of fourteen matched controls using growth curve analysis. The learning curve and recognition performance of the aphasia group was significantly below the matched control group, although above-chance recognition performance and case-by-case analyses indicated that some participants with aphasia had learned the correct word-referent mappings. Verbal short-term memory but not word processing abilities predicted word learning ability after controlling for aphasia severity. Importantly, participants with lesions in the left frontal cortex performed significantly worse than participants with lesions that spared the left frontal region both during word learning and on the recognition tests. Our findings indicate that some people with aphasia can preserve the ability to learn a small novel lexicon in an ambiguous word-referent context. This learning and recognition memory ability was associated with verbal short-term memory capacity, aphasia severity and the integrity of the left inferior frontal region.