The Beatles and Cassius Clay The Beatles and Cassius Clay

Their timing was as perfect as their music. The Beatles' first trip to America in February 1964, just a few weeks after the assassination of President John F. Kennedy, brought a devastated nation some desperately needed joy and excitement — and that's just one of the many seismic events in the new American Experience documentary 1964, premiering Tuesday on PBS (8/7c, check local listings).

What a year. President Lyndon Johnson spearheaded the landmark Civil Rights Act and launched a war on poverty, students at U.C. Berkeley were rising up in revolt, millions flocked to the futuristic New York World's Fair, Betty Friedan was triggering a feminist firestorm with The Feminine Mystique and Bob Dylan told us — as if we needed further proof — that The Times They Are a-Changin'.

Based on the Jon Margolis book, The Last Innocent Year: America in 1964, the program is narrated by Oliver Platt and features a terrific but little-known story about the day the Beatles met up with the year's other intergalactic superstar, Cassius Clay — who would soon announce his conversion to Islam and change his name to Muhammad Ali.

Check out this exclusive clip of the Fab Five's fascinating meeting!