:thinking: I didn't realize that I needed one of these until I saw it.
Umm, why don't you try to crochet it? Look up "how to crochet" on about.com. I taught myself to crochet from a book years ago (it's WAY easier than knitting).
I realize that the point is that you want to KNIT something, so here's my idea. Using small needles, knit a rectangle approximately 6" x 2 1/2", fold in half lengthwise and seam the two sides. You'll probably have to tweak the measurements to get it to fit snugly around the chapstick. (I did measure one, but everybody's tension is different.) You could just make a braid out of three or more strands of yarn and tie it to the rim for the loop.
On the needles: Tempting for Kate, cabled jacket for Emma