Hi Jim, you'll need to create a solid that is pushing downwards a ways into your object and then use that solid as the cutting object in boolean difference to cut it away from the main piece.

But since you want a piece that follows the same general shape as the original outer surface, you'll probably want to build that cutting object solid by trimming out a small portion of that original outer surface and then probably using Extrude to extrude that smaller surface fragment into the cutting object.

See this previous post for an example:
http://moi3d.com/forum/index.php?webtag=MOI&msg=3024.4

Also check out here for some ideas on cutting grooves into things:
http://moi3d.com/forum/index.php?webtag=MOI&msg=3859.2

- Michael