No, they don't have a gearbox (yet).

What the current generation of engines have is two or three co-axial shafts rotating at different speeds.

The difference in shaft speeds is achieved by varying the size, shape and placement of the turbine blades connected to the shaft, not with a gearbox.

(And a single gear in isolation would be pointless. By definition, the purpose of a gear is to mesh with another gear.)

Here's an informative video: http://www.youtube.com/watch?v=zy4A-z2WKhw