Chamfer to curve at distance.

can you show a photo ?

FredSWUG's answer would be the best for an actual chamfer.

You could use the Variable Fillet option and instead of a Circular profile choose a Conic Rho profile. the closer your Rho value is to zero the closer it gets to a chamfer. Try starting with a Rho value of 0.05. This may be a little easier to adjust and tweak to get the desired results and it tied to to edges and can follow tangency. Also different points can have different Rho values so one end could be flatter with the other end more round.

A picture of what you have tired and the results you are looking for would also help.

best sweep it, at the end create a sketch, then rotate subtracting. not that much of an effort......

Not with the chamfer tool.
I think the best result would come by using the sweep command, but there are different ways to get such a result. It is difficult to give a precise solution without seeing the model.

Use sweep or revolve or path extrusion or path rib command. Before apply these commands create your desire profile shape as you want.