Just wanted to note for future reference that this feature has been added (and buried) in Illustrator CC.
First, apply the gradient to a stroke instead of a fill. Because you can do that now
In the gradient panel, there's a sub-option for "stroke", and the middle option is "apply gradient along stroke."
If you make the stroke width the same as the diameter of the circle, this will achieve the desired result.
Here's a screenshot of what I came up with. Obviously the reds on my gradient need to match.
