Chwast was born in the Bronx, New York City[1] and in 1948 graduated from Abraham Lincoln High School in Brooklyn where he was introduced to graphic design by his art teacher, Leon Friend.

After graduation, he went on to hold several jobs, which included working on promotional art for the New York Times.

He also worked at Esquire magazine, where he reunited with fellow Cooper Union alum Edward Sorel.

[1][3] Chwast is famous for his commercial artwork, which includes posters, food packaging, magazine covers, and publicity art.

In 1970, he met Paula Scher during an interview she had with him at Pushpin while she was still a senior at Tyler School of Art.