Like more early Rolling Stones than is acknowledged, "Time Is On My Side" is quite the slow ballad, but one which has a lot of insouciant blues-soul, particularly in Mick Jagger's drawn-out, drawling delivery.
The song starts - at least, the most familiar version of it starts (more on this later) - with a piercing, memorable drawn-out bluesy guitar lick, both spiritual in its arch and raunchy. But the Rolling Stones did make it their own, with a reinterpretation that was more substantial, and substantially different from the original, than most of their early covers. Like most of their early recordings, it was a cover, this one of a single by the great New Orleans soul singer Irma Thomas. "Time Is On My Side" was the first really big American hit for the Rolling Stones, reaching #6 at the end of 1964.