In early October, CME Group Inc. Chief Executive and Chairman Terrence Duffy met with one of his top lieutenants and set in motion a risky plan that the exchange operator had been secretly developing for two years: launching a futures contract based on bitcoin.

That plan was unveiled this week, and represented a big step toward bringing the highly volatile digital currency into the financial mainstream. Bitcoin, which only started trading in 2009, has long been a niche market and continues to be tarnished by its association...