Here is an answer from a Stihl saw FAQ:
Why does my saw leak bar oil?
The way our units lubricate a chain, most of the oil is distributed around the inside of the bar rails as it is circulated by the oil reservoirs in each drive link of the chain. The amount of oil being circulated inside the bar at any given time can be between .3 and .5 oz. As a general rule of physics, the oil will be pulled down by gravity once the chain stops turning, collecting at the bottom of the bar and seeping through the chain to puddle underneath the bar & chain assembly as well as under the drive sprocket. The fact that it appears to be continuing to seep after the unit is cut off for several days is owed to the viscosity of the oil and the anti-flinging compound (lithium) mixed with the oil at the refinery. These factors give the oil a very thick consistency, which in turn explains a slower flow rate. This condition is deemed to be normal for any chainsaw with a similar bar & chain lubricating system.
If the unit continues to seep oil after a few days, the problem may be the vacuum relief valve located in the side of the engine housing between the oil output hole and the bar stud(s). This valve has an internal spring and ball type arrangement with the ball pressed against the vent hole of the casing of the valve, when the tank develops a vacuum from the normal process of the oil being pumped out. The ball is pulled away from the hole, allowing air to enter into the tank and break the vacuum so that oil can continue to flow to the bar and chain assembly. Once the vacuum is relieved, the spring pushes the ball back against the hole of the valve casing. Sometimes debris may become trapped between the ball and the hole. This would cause the oil to keep "weeping" because there must be some measure of vacuum in the tank to keep the oil from flowing freely once the unit is shut down. More often than not, all one needs to do is to take a small pin or needle and push it into the hole of the valve (identifiable as a small silver disk with a small hole in the center) about 6 or 7 times to loosen the debris. This should re-seal the orifice and keep the oil from seeping from the output hole when the saw is stored.