You are like the fifth person to mention this to me this week! 4 others in my gym are having similar problems and I myself have been battling this "injury" for 6 months now. In my case, it seems to originate at the brachioradialis tie in just beneath the bicep, but tends to radiate through the entire bicep when it becomes inflammed. Popping 600 mg of ibuprofen an hour before my workout has proven quite effective. I was told at one time that it was the result of a strength imbalance between the tendon and the muscle that could be corrected by careful use of static contraction. The fact that we can both continue to train aside from the discomfort seem to indicate more of a tendinitis type of situation than a severe tear. The first time I felt it was after an armwrestling meet, and then I really aggravated it with some very heavy hammer curls. Hammer curls, iso-lateral curls (obviously) and reverse curls seem to inflame the area much more for me than traditional barbell curls. Tendons heal at a very slow rate being that the tissue is avascular or lacks the circulatory component of muscle tissues, and in my experience these types of injuries can continue to produce pain years after the injury regardless of the amount of healing.
I would start a daily regimen of joint supplementation including glucosamine, chondroitin, MSM, and or gelatin if you already aren't using these things. I have also discovered that refraining from using the affected area only makes it worse, and that it's better to do rehabilitating light weight-high rep work instead of none whatsoever. Avoid abrupt jerky movements with the weights or when using the arm at all and maybe with the above recommendations you will see at least some degree of improvement over time as I have. Certain AAS when used intelligently can also aid in the repair process.
"I believe a man does what he can, until his destiny is finally revealed."