This is most likely Tuckahoe Marble. If it is then it originated from a now closed quarry hole in the ground north of New York City in Westchester County. This stone represents one of the earliest marbles commonly used in America and predates the discovery of marbles in Vermont. There is a whole lot of history associated with this stone.
It is a stone that was used in the 19th c on a number of buildings, most prominently Tweed Courthouse (connected to the political corruption of the Tweed Ring), Brooklyn Borough Hall, Grace Episcopal Church (where Tom Thumb and Lavinia Warren were married), the Washington Memorial Arch and Federal Hall. Over the years I have worked on several facades and structures that have this marble in it.
This particular chunk came from a demolition underway at Snug Harbor Cultural & Botanical Gardens on Staten Island. This site, comprised of a complex of buildings, was formerly known as Sailor's Snug Harbor, a 19th c haven for worn out and retired sailors. Currently a National Historic Landmark. This chunk was a portion of a much larger earth, concrete and stone removal underway and was quickly being loaded into a dump truck to be hauled off to a landfill. We were working on a nearby building when I managed to grab a piece before it got loaded and hauled off.