ˈælən wʌz bˈɔːɹn ˌɔn mˈeɪ fˈaɪv, wˈʌn θˈaʊzənd ˈeɪthˈʌndɹɪd fˈoːɹɾi wˈʌn, ɪn fɪlɐdˈɛlfiə tə kwˈeɪkɚ pˈɛɹənts: dʒˈɑːn kˈæsdoːɹp ˈælən, ɐ pɹˈɑːmɪnənt dɹˈʌɡɪst, ænd ɹᵻbˈɛkə smˈɪθ lˈiːdz, hɪz wˈaɪf.
Allen was born on May 5, 1841, in Philadelphia to Quaker parents: John Casdorp Allen, a prominent druggist, and Rebecca Smith Leeds, his wife.