GordonGekko

Sorry, an offset or eccentric choke is a custom choke (Briley and several other companies make them), that is thicker on one side than on the others. They are used to correct bent or non-concentric (the bore is not centered in the barrel) shotgun barrels or chokes, and are used mostly on O/U's and SxS's where one barrel is patterning to a drastically different POI than the other. They can get pretty expensive though and you'd have to send your gun to Briley (or at the very least the barrel), they are really a last resort if you are sure that your gun fit is perfect. Come to think of it you might come out better just getting a new barrel from Winchester

Gordon