As far as I know, you need a Kenmore that takes the needle plate inserts (there are several models that use an insert. The inserts are for straight or zigzag stitching....little round hole on one end & zigzag slot on the other You just remove them & turn them around for one or the other. There are also several different inserts for various models). So what I'm saying is if your machine doesn't have an insert like this for regular sewing (in other words, just has the standard 1 piece needle plate), the zigzag attachment won't work.
I have a 158.1755 that has one type of needle plate insert for normal sewing....& here it is
http://www.ebay.com/itm/KENMORE-NEED...item5b02724967 It does really nice chain stitching. If your machine normally has one of these inserts, you might just need a chain stitch kit with a different insert. And yeah. the silver gizmo will fit anyplace a class 15 bobbin case does.