Some thoughts:
It's possibly a sign of either poor form (using your front shoulder to do some of the work instead of the biceps) or using too heavy a weight ( so, again, the shoulders have to pitch in). Try doing the bicep work with dumbbells, making sure to keep your elbows glued to your side (they may move a bit, but not too much). Also, make sure that your shoulders are "back and down" (that scapular contraction that Cathe always tells us about), because I think that maybe if they are rounded a bit toward the front they will be more apt to carry some of the weight.