Okay, so no cable, which is what I was originally thinking and what Cbjr was writing.
However, there is a bit of linkage behind that knob which could gum up the works. Hit the pivot and other rubbing points with some spray lubricant. (not WD-40!) if that doesn't free it up, then you may have to remove the choke linkage, pull the enricher valve plungers (the parts in the carb that move when you pull the choke knob) and clean it all up.
Currently Running Stable:
2010 Honda NT700V
1986 Shadow 700
1986 Honda Trail 110 (Postie Bike)
1987 Honda Rebel 450
1973 Honda Mini Trail 50