This paper examines the predictions made by Chinese, Muslim and Jesuit astronomers of the eclipse of 21 June 1629 in Beijing, allegedly the event that determined Emperor Chongzhens resolution to reform the calendar using the Western method. In order to establish the accuracy of these predictions, as reported at the time by the Chinese scholar and convert Xu Guangqi, we have compared them with an accurate reconstruction of the eclipse made at NASA. In contrast with current opinions, we argue that the prediction made by the Jesuits was indeed the most accurate. It was in fact instrumental in dissipating Chongzhens doubts about the need to entrust Jesuit missionaries serving at the Chinese court with the task of reforming the calendar, leading to the first important scientific collaboration between Europe and China.