According to American Songwriter, Randy Bachman of the Guess Who was in a car with Burton Cummings driving from gig-to-gig and kept hearing one of the Bee Gees' first big hits, "New York Mining Disaster 1941," on the radio.

Bachman played off of the riff and eventually came up with what we know as "Laughing." 

"To pass the time, Bachman started strumming the opening chords to the Bee Gees song, but he started changing the notes ever so slightly to create a slightly different feel. As he endlessly fooled around with it, Cummings began to get annoyed and suggested they write some lyrics to the thing already."

The rest of the story can be found here.