Happiness is like a butterfly: the more you chase it, the more it will elude you. But if you turn your attention to other things, it will come and sit softly on your shoulder.
Source, in full
According to The Quote Investigator, "the earliest instance of this saying was crafted by the enigmatic "L" for "The Daily Crescent" newspaper in New Orleans [in June 1848]. ... The linkage to Henry David Thoreau is unsupported."