Giovanni Battista Gaulli’s dome fresco in the church of Santissimo Nome di Gesù, the mother church of the Society of Jesus, which he carried out between 1672 and 1675, is widely recognized as one of the most spectacular examples of Roman Baroque painting. According to most scholars, the fresco should be seen as a ‘collaborazione a tre’, a three-way collaboration between Gian Paolo Oliva, as the patron who invented the iconographic program; Gian Lorenzo Bernini, as the designer of the fresco; and Gaulli – better known by his nickname Baciccio – as its executant. But is this, in fact, a valid way of understanding how the work came into being? Did the painter merely carry out Oliva’s program and Bernini’s designs? Or, should more creative agency be given to Baciccio for originating the design of the work? In an effort to answer these questions and to define, to the extent that it is possible, the particular role each of these individuals played, this essay revisits the history of the dome fresco project. And through a careful re-examination of the relevant primary and secondary sources, and, more importantly, all of the surviving preparatory drawings and bozzetti, the author presents a more nuanced and more accurate picture of what each of the three men contributed to the project, and argues that Baciccio, in fact, assumed the generative role in giving visual form to Oliva’s program and designing the imagery for the dome fresco.