Julia Augusti Filia (39 BC - 14 AD), the daughter of Augustus and second wife of Tiberius, was accused of adultery and licentiousness, and exiled, on Augustus's orders, to the island of Ventotene in 2 BC. Both Cassius Dio (in The Roman Histories) and Seneca (in On Benefits) refer to her conducting "revels" and "debaucheries" in the Forum, "and even on the Rostra," with a number of male partners. Seneca explicitly states that she prostituted herself.
The Rostra was a platform at the western end of the Forum, and was the point from which orators, including Emperors, addressed the masses. Although secular in nature, it had a near sacred significance to the Roman state. It was a place where no woman should ever have been seen, and on which no man should be seen without a toga. The equivalent would be a member of the British Royal Family fornicating in the middle of Trafalgar Square. This specific claim, however, may well have been apocryphal.
Elaine Fantham's book, Julia Augusti (Routledge 2006), gives a balanced historical account of her life).