When Louis Pasteur remarked that chance favours the prepared mind, he was commenting on the important role played by serendipity in scientific discovery. That role is well known (most know of the story of Fleming's accidental discovery of penicillin) but much of the literature focuses on the STEM disciplines, on 'big' science, and concentrates on the work of established scientists. There is virtually no discussion of the role of serendipity in the doctoral research arena, an arena which contributes significantly to contemporary scientific endeavour and the associated publications. This article reports the initial results from a survey of doctoral students and PhD graduates which explores how serendipity contributes to the PhD process and also the forms serendipity takes in this arena. Following the conceptual differentiation of serendipity from accident or chance, the article explores the intersection of serendipity with doctoral research. Most respondents reported serendipitous occurrences happening in the doctoral experience, with the most important involving them stumbling across unexpected and unsearched-for literature, meeting others who proved to be significant for both their research and also their future development and careers, and finding project-related artefacts which expanded their projects and thinking. There were also reports of second-hand serendipity a hitherto uncommented on phenomenon. Many of the serendipitous occurrences involved a social context and actors other than the doctoral student, placing a focus on the researcher as someone with the ability and opportunities to make connections rather than simply relying on luck.