Also known as: Vandyke chain stitch
This stitch is the incorporation of chain stitch in a zig zag manner. In other words, a zig zag chain stitch is done between two parallel lines instead of one. Ideal for any border embroidery, this is more of a decoration stitch.

I have used only one stitch line to illustrate this stitch. You may imagine a parallel stitch line over the one that I have marked. To do this stitch, you need to know how to do chain stitch.

zig_zag_chain_stitch_1           zig_zag_chain_stitch_2
Fig 1: With the base on the stitch line, do a chain stitch loop.   Fig 2: The stitch should be slanted at about a 45 degrees angle, from the stitch line. If it helps, you may draw a parallel stitch line as well.

zig_zag_chain_stitch_3 Fig 3: Continue with the chain stitch procedure, but keep the needle at a 45 degree angle always, for every new stitch.

Fig 4: You should get a pattern like this when done on a straight line. You can try to follow curves too.