O'Neill was born on June 25, 1874, in Wilkes-Barre, Pennsylvania, the second of seven children to William Patrick, an Irish immigrant, and Alice Asenath "Meemie" Smith O'Neill.
Within two years, O'Neill was providing illustrations for the local Omaha publications Excelsior and The Great Divide as well as other periodicals, having secured this work with help from the editor at the Omaha World-Herald and the Art Director from Everybody Magazine who had judged the competition.