Radio monitoring of the broad absorption line quasar (BALQSO) Mrk 231 from 13.9 GHz to 17.6 GHz detected a strong flat spectrum flare. Even though BALQSOs are typically weak radio sources, the 17.6 GHz flux density doubled in ~150 days, from ~135 mJy to ~270 mJy. It is demonstrated that the elapsed rise time in the quasar rest frame and the relative magnitude of the flare is typical of some of the stronger flares in blazars that are associated with the ejection of discrete components on parsec scales. The decay of a similar flare was found in a previous monitoring campaign at 22 GHz. We conclude that these flares are not rare and indicate the likely ejection of a new radio component that can be resolved from the core with Very Long Baseline Interferometry. The implication is that Mrk 231 seems to be a quasar in which the physical mechanism that produces the BAL wind is in tension with the emergence of a fledgling blazar.