It seems like some are a little confused about what Triskellion is saying, so I will try to help out with what I know (admittedly not a great amount) about the subject.
General Relativity does predict a time dilation effect from variations in gravitational acceleration, however this should not be a significant cause of dilation measured by clocks at varying altitudes (at least not compared to the alternative). As you probably know the acceleration due to gravity on a body at higher elevation is lessened. This however if responsible would reverse the observations so that the clock at sea level would seem to count more slowly relative to another at altitude.
The cause of the dilation in this case is a variance in velocity, not acceleration. Velocity at higher altitudes is greater than that at lower ones, compare the earths rotation with that of any circular object and it is easy to observe why. Every point along the radius of the circle must complete each rotation together in the same duration of time. A point with a greater radius must travel a longer distance around its circumference than one with a shorter radius. The point at the greater radius/elevation must therefore travel at a higher velocity than a lower point.