What Wikipedia says: "Jay-Z was also involved in several battles with rapper LL Cool J in the early '90s." - Wikipedia
The always-great Combat Jack dropped this nugget onto his blog in 2009, but it's still amazing to read here and now. For those who don't know, Combat was Dame Dash's lawyer for many years; he's got...stories, ha.
This particular yarn goes back to 1992, when Dame Dash and Clark Kent figured "if Jay was known as the dude that kilt LL in battle, record labels would take note and give him that much sought after deal. Whenever LL was spotted by either of them, they would page each other and Jay and get him to meet at whatever location LL was. This went on a couple of times. Once contacted, Jay would roll up to the club, bar or whatever venue and lay in the cut, waiting for his opportunity to attack LL in battle. Dame would polly with, then taunt LL about how Jay was nicer than him, was ready to take his spot even. LL's ego would result in him agreeing to go head to head against the young and then unknown challenger."
And, Combat Jack said, Jay Z pulled off the impossible and won each time, which is why he thinks LL resents him to this day.