We conducted a records-based cohort study of patients who initiated pre-exposure prophylaxis (PrEP) at a large federally qualified health center in Los Angeles, CA to characterize patterns of PrEP use, identify correlates of PrEP discontinuation, and calculate HIV incidence. Of 3121 individuals initiating PrEP between 2014 and 2017, 42% (n = 1314) were active (i.e., had a current PrEP prescription) in April 2018. HIV incidence was 0.1/100 person-years among active PrEP patients, compared to 2.1/100 person-years among patients who discontinued. Compared to patients accessing PrEP through government programs with no prescription copay, risk of discontinuation was higher among those with private insurance (ARR = 1.4, 95% CI 1.2, 1.7), or no insurance (ARR = 4.5, 95% CI 3.2, 6.4). Sixty-three percent of active PrEP patients had gaps between PrEP prescriptions, averaging one gap per year (median length = 65 days). Increasing access to free or low-cost PrEP can improve PrEP continuity.