All existing databases of spoofed speech contain attack data that is spoofed in its entirety. In practice, it is entirely plausible that successful attacks can be mounted with utterances that are only partially spoofed. By definition, partially-spoofed utterances contain a mix of both spoofed and bona fide segments, which will likely degrade the performance of countermeasures trained with entirely spoofed utterances. This hypothesis raises the obvious question: ‘Can we detect partially spoofed audio?’ This paper introduces a new database of partially-spoofed data, named PartialSpoof, to help address this question. This new database enables to investigate and compare the performance of countermeasures on both utterance- and segmental- level labels.