We developed and tested an NSF IGE-funded year-long program to improve the oral communication skills of STEM graduate students. By the end of the program, we organized our curricular materials into a 3C framework: "connect, convey," and "captivate." Within this framework, the Fellows learned rhetorical strategies, created podcasts, regularly practiced improvisation, and provided each other with extensive feedback about their work. The Fellows in cohorts one and three gave public presentations followed by a question-and-answer period. Formative and summative assessments were built into the curriculum, including the use of the Public Speaking Competency Rubric (PSCR), and a calculation of jargon. Fellows also longitudinally self-reported their anxiety levels and apprehension of public speaking. The Fellows performed well according to their PSCR scores, but they also reported a slight increase in anxiety levels; the project, as well as the study, were confounded by the COVID-19 pandemic. Public audiences rated cohort three highly on all 3C items. Graduate students in STEM perform research that is of interest and significance to society, and the STEM Storytellers program helped them better translate their research to engage these broader audiences in meaningful conversation.