I first saw this stitch in one of my favourite stitch handbooks The Stitches of Creative Embroidery by Jacqueline Enthoven. It's an older book (first published in the 60's I think) and perhaps not as fancy looking as modern craft books but it offers lots of ideas for stitch variations.
The Zig Zag Long Stemmed Chain Stitch is basically a bunch of detached Chain Stitches with long stems, placed at an angle to achieve a (slight) Zig Zag effect. If you are not familiar with the detached Chain Stitch yet, check out this tutorial I posted earlier this year.
The main difference between a regular Detached Chain Stitch and the Long Stemmed Chain Stitch is that instead of anchoring your loop (or 'chain') with a tiny stitch (regular) you use a longer stitch ('stem') to anchor the chain. The first photo shows the long stem clearly.
To create the Zig Zag effect, the next step is to make another Long Stemmed Chain Stitch. Place it at an angle to the left or right of the stem of your first stitch. You can use the stem of the first stitch as a guide for placing the stitches of your second Long Stemmed Chain Stitch. The top of the stem is about the same level as the pointy bits of your chain. The chain of the second stitch is anchored right below the stem of the first stitch (second photo). Repeat the first two steps, alternate left and right (third photo) until finished, ending with a stem.
You can vary the angle of your chains and stems to create different effects or even a curvy Zig Zag Long Stemmed Chain Stitch (fourth photo).