In a city known from producing fake rain (remember the sprinklers on MoPac near 35th Street?) and celebrating Spamarama, it should be no surprise that Janet Gilles can stand under a light pole on Town Lake and chirp without causing much of a fuss. She calls out for monk parakeets seen grooming just before they leave their nests to eat. They chirp back. Gilles release 19 monk parakeets, natives to Argentina, in March of 1991 when they wore out their welcome as house pets.
Those sites describe this story as an urban myth, but that designation "suggests nothing about the story's veracity".