Cheley: I don't own that book so I can't refer to it, but I agree with Dee that she is probably describing a technique that simply has you tighten up the second stitch of the row a little bit (no slipping involved). In the version I use, you do the first stitch normally, and then stick the right needle point into the next stitch as usual, but before completing it, tug a little on the working yarn to tighten. (I think keeping the right needle point under the stitch while pulling keeps it from getting too tight.)
A slipped stitch selvage is easier to do (IMO), but there may be times when you don't want a chain selvage because it doesn't match, or makes the edge tighter than you'd like.
If your edges are still loose when you do the second stitch tightening thing, you can also try to just consciously knit the last few stitches of a row a little more tightly than usual. That's supposed to help too.
Sue: This is something I've read up on (can you tell?) because loose edges really bug me. There are several ways to get a chain selvage, and all of them look pretty similar, but according to one source, the "technically superior" one when using stockinette is to slip 1 knitwise on knit rows and slip 1 purlwise on purl rows. (The last stitches of a row are not modified at all so the last stitch of a knit row will be a knit, and the last stitch of a purl row will be a purl.) It's different from what you've been doing, so you might want to try it and see whether you get a better result. The main advantage to this particular method over other chain methods is that your working yarn will be in the correct position when you start the next row -- though it sounds unlikely, it's conceivable that less manipulation of the working yarn will result in less looseness for you. Who knows? It's worth a shot, anyway. You can try the tightening the second stitch thing too.
P.S. Where did you happen to get your chain selvage instructions? It's not a version I can find in any of my books. Is it possible you mis-read it? If so, that could be the source of the problem. :shrug: