Scholars at the Great Library of Alexandria unanimously deemed Aeschylus to be the author of Prometheus Bound. Since the 19th century, however, several scholars have doubted Aeschylus' authorship of the drama. These doubts initially took the form of the so-called "Zeus Problem." That is, how could the playwright who demonstrated such piety toward Zeus in (for example) The Suppliants and Agamemnon be the same playwright who, in Prometheus Bound, inveighs against Zeus for being a violent tyrant? This objection prompted the theory of a Zeus who (like the Furies in the Oresteia) "evolves" in the course of the trilogy. Thus, by the conclusion of Prometheus the Fire-Bringer, Aeschylus' Zeus would be more like the just Zeus found in the works of Hesiod.
Increasingly, arguments for and against the attribution to Aeschylus have been based on metrical-stylistic grounds: the play's diction, the use of so-called Eigenworter, the use of recitative anapests in the meter, etc. Using such criteria in 1977, Mark Griffith made a case against the attribution. C. J. Herington, however, repeatedly argued for it. Since Griffith's landmark study, confidence in Aeschylean authorship has steadily eroded. Influential scholars such as M. L. West, Alan Sommerstein, and Anthony Podlecki have made arguments against authenticity. West has argued that the Prometheus Bound and its trilogy are at least partially and probably wholly the work of Aeschylus' son, Euphorion, who was also a playwright. Based upon allusions to Prometheus Bound found in the works of comic playwright Aristophanes, Podlecki has recently suggested that the tragedy might date from c. 415 BC. Those who trust in the verdict of antiquity and still favor Aeschylean authorship have dated the play anywhere from the 480s to 456 BC. The matter may never be settled to the satisfaction of all. As Griffith himself, who argues against authenticity, puts it: "We cannot hope for certainty one way or the other."
The argument of Herrington and others for authenticity has largely centered upon the fact that Prometheus by Aeschylus was the first play in a trilogy and therefore discussion of its isolated attribution are of limited import. Of all Aeschylus plays and tragedies, which have been numbered by some as approaching ninety plays during his own lifetime, only the Orestia trilogy survives in the complete text of all three plays among the seven surviving plays by Aeschylus.