https://www.boston.com/sports/boston-marathon/2018/04/06/baa-unicorn-symbol-history-boston-marathon
"“It’s probably one of our most frequently asked questions,” Jack Fleming, the BAA’s chief operating officer, said of the unicorn’s origin with the athletic association, which organizes the marathon. “People pause on it, they think about it.”
He said the common belief is that the unicorn was on the family crest of one of the BAA’s founding members.
“That hasn’t been proven,” Fleming said. “But with the rich heritage up here — between the Scots and the English and the Irish, it’s a pretty good likelihood.”
"The athletic club was founded in 1887 (the first Boston Marathon took place in 1897), and the unicorn was associated with all the organization’s sports."