A Client asked me to make some arts-and-craft style picture frames that incorporated the traditional square peg. This was enjoyable work using my Lie-Nielsen 1/4" bevel edge socket chisel.
It is good practice to cut across the grain when squaring circles. Most importantly, it is unlikely to split when cutting in this orientation. Secondly, the end grain provides firm resistant for the chisel and terminates in a clean, crisp cut at the bottom of your hole.