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Here is the answer plain as day... I've overlooked this for hours.
See help file: Clip command (editing toolbar)
You have a lot of options which may differ depending on if the polygons are in the same dataset or not. Here's a few.
If they are in the same dataset, you can select the polygon you want to keep as is, and use the Editor - Clip tool to remove the overlap in the other polygon.
If they are in different datasets, and you have ArcInfo, you could select the polygon to keep as is and use the Construct Features - Split polygon to cut up the other polygon into overlap and non overlap areas, and then delete the overlap. Or in you don't have ArcInfo, you could use the Cut Polygons Without Selection Task (a great tool which is in the developer kit samples) and select the polygon to keep as is and trace its outline to cut the polygon up and then delete the overlapping area.