The eyes are made from thick, green-tinted glass. Green LEDs were installed behind them in a 2007 restoration. Before then, incandescent bulbs sat in the owls’ skulls and projected as green through the glass, Don Bussolini, a capital projects director for the 34th Street Partnership, said.

How these green-eyed owls first came to be is stranger than most would imagine.

The two owls were once part of a flock of 22 that roosted along the roofline of the old New York Herald newspaper building, for which the square was named. The owls lit up on the hour with the ringing of a clock bell that was part of the building.

The Herald was one of the most popular American newspapers for much of the 19th century, and the current owls in the square rest on a monument dedicated to its founder and publisher, James Gordon Bennett, and his son and successor, James Gordon Bennett Jr.

While the elder Mr. Bennett’s legacy is that of a pioneering newspaperman, his son’s is that of a clever but eccentric playboy who inherited the newspaper when he was in his mid-20s. He apparently enjoyed riding his horse-drawn coach at full-speed down country roads while naked and yelling, and among his quirks was an obsession with owls.