To make the Cube editable, convert it to an Editable Poly (Right-click > Convert To: > Convert to Editable Poly).
Add a MeshSmooth modifier to our object. Set the Iterations to 3. You can see now that our object has a barrel shape. That's because it has been smoothed according to its geometry. If it was a 1x1x1 cube, the smoothed shape would've been close to a sphere, but the 2 extra segments make the difference in this case.
Time to actually chamfer some edges, right? I had to change the colour of my object so you can see better what I'm about to do. Go back to our object, switch to Edge editing mode (hit "2" on the keyboard) and select the edges that define the front face. Hit the Chamfer Dialog button and enter 0.1 in the Chamfer Amount box. Hit OK. Not a big difference, right? But when you go back to the top modifier (MeshSmooth) your object looks now much different. The edge you chamfered created a much sharper edge and an almost flat face on the smoothed object.
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