A dataset of measured headphone transfer functions (HpTFs), the Princeton Headphone Open Archive (PHOnA), is presented. Extensive studies of HpTFs have been conducted for the past twenty years, each requiring a separate set of measurements, but this data has not yet been publicly shared. PHOnA aggregates HpTFs from different laboratories, including measurements for multiple different headphones, subjects, and repositionings of headphones for each subject. The dataset uses the spatially oriented format for acoustics (SOFA), and SOFA conventions are proposed for efficiently storing HpTFs. PHOnA is intended to provide a foundation for machine learning techniques applied to HpTF equalization. This shared data will allow optimization of equalization algorithms to provide more universal solutions to perceptually transparent headphone reproduction.