On the purl rows, slip the first stitch purlwise, purl to the last stitch then knit the last stitch of the row.
A good link describing 'chain selvedge' can be found here
A little word of caution though. By doing this, you will only have half as many 'stitches' along each edge for picking up since the edge stitches are only actually knitted every other row. You have to make sure that this will be enough stitches to use for picking up. Generally when I'm picking up stitches along an edge I'll pick up stitches on approx 4 out of every 5 rows or sometimes 3 out of every 4 rows, depending on the project. So if you've done a slip stitch edging and are intending to pick up stitches, even if you pick up in every loop you will only be doing 1 out of every 2 rows. Does this make sense? I just worry that you'd end up with a bunchy edge that wouldn't lay quite flat with the number of stitches you'd end up with.