Where did the phrase 'march to the beat of a different drummer' originate?

It is derived from the writings of the American philosopher Henry David Thoreau, who wrote:

"If a man loses pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured, or far away. "

Thoreau is the author of the expression, which has entered the language and appears in various forms. The form you mention is probably the most commonly heard.