Authorship verification is the problem of determining if two distinct writing samples share the same author and is typically concerned with the attribution of written text. In this paper, we explore the attribution of transcribed speech, which poses novel challenges. The main challenge is that many stylistic features, such as punctuation and capitalization, are not available or reliable. Therefore, we expect a priori that transcribed speech is a more challenging domain for attribution. On the other hand, other stylistic features, such as speech disfluencies, may enable more successful attribution but, being specific to speech, require special purpose models. To better understand the challenges of this setting, we contribute the first systematic study of speaker attribution based solely on transcribed speech. Specifically, we propose a new benchmark for speaker attribution focused on conversational speech transcripts. To control for spurious associations of speakers with topic, we employ both conversation prompts and speakers' participating in the same conversation to construct challenging verification trials of varying difficulties. We establish the state of the art on this new benchmark by comparing a suite of neural and non-neural baselines, finding that although written text attribution models achieve surprisingly good performance in certain settings, they struggle in the hardest settings we consider.