He could run and swim — but he couldn’t hide.

A gun-toting motorist fleeing from a traffic stop last night in Washington Heights dove into the East River and miraculously survived a 1,000-foot swim across the choppy waters to The Bronx, police sources said.

As police approached Chauncey Kautz, 23, at West 181st Street and Amsterdam Avenue, he jumped out of his vehicle, ran through Highbridge Park, allegedly ditched a loaded 9 mm handgun — and then dove into the East River.

Once he washed ashore in The Bronx, he took off on foot again. He was finally nabbed by cops who tackled him and ended the chase.