Try using support loops instead of a chamfer. Not the greatest topology but only took like 30 seconds and looks good enough imo.
And if you ever want a chamfer there you just need to have some (equidistant) support loops around it. Same reason you should add double support loops but more extreme.
Joost thank you for your demonstration. The concave edge works really well. How would you deal with the edge that carries over to the other side that's breaking the roundness? Would you try to end them somewhere along the way not letting them reach the other side?
Is this the shape you're trying to create? topology is a bit cleaner thanks to seb's suggestion. Also I found that I needed more segments in the curve to keep everything equidistant and maintain the curve.
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And if you ever want a chamfer there you just need to have some (equidistant) support loops around it. Same reason you should add double support loops but more extreme.
max file here:
https://dl.dropboxusercontent.com/u/2333222/thing.max