Pandemic influenza remains a serious public health threat and the processes involved in the evolutionary emergence of pandemic influenza strains remain incompletely understood. Here, we develop a stochastic model for the evolutionary emergence of pandemic influenza, and use it to address three main questions. (i) What is the minimum annual number of avian influenza virus infections required in humans to explain the historical rate of pandemic emergence? (ii) Are such avian influenza infections in humans more likely to give rise to pandemic strains if they are driven by repeated cross-species introductions, or by low-level transmission of avian influenza viruses between humans? (iii) What are the most effective interventions for reducing the probability that an influenza strain with pandemic potential will evolve? Our results suggest that if evolutionary emergence of past pandemics has occurred primarily through viral reassortment in humans, then thousands of avian influenza virus infections in humans must have occurred each year for the past 250 years. Analyses also show that if there is epidemiologically significant variation among avian influenza virus genotypes, then avian virus outbreaks stemming from repeated cross-species transmission events result in a greater likelihood of a pandemic strain evolving than those caused by low-level transmission between humans. Finally, public health interventions aimed at reducing the duration of avian virus infections in humans give the greatest reduction in the probability that a pandemic strain will evolve.