Chicken scratch embroidery (also called snowflaking, Tenneriffe lace, or Amish embroidery) is a form of cross-stitch that is done on gingham fabric using the edges of the squares instead of counting threads. It's usually done with white thread so the end result looks like lace. You can also work the designs with thread that is the same color as your gingham—this is called reverse chicken scratch.
The technique uses three simple stitches—the double cross-stitch, the straight running stitch, and the woven circle stitch. I'll show you all three.
Double Cross Stitch
Work a cross stitch from corner to corner in one square of the gingham. If you're using the darker color for reverse chicken scratch (in this case, red), work in the white blocks.
Then work a straight cross stitch over this. Remember to do your cross stitches in the same order so all your threads go in the same direction.
I talked about running stitch a while ago and this is essentially the same thing. Working from right to left, take a stitch from one side of each gingham square to the other, skimming under the squares in between.
Woven Circle Stitch
Bring your needle up in the same hole as the running stitch. Slip the needle under the running stitches to form a circle.
Go around the circle a second time, then insert your needle in the same hole that you started from.
Here's what they look like together.
These pictures are of a lavender gingham apron that's for sale on my website. Very simple design with rows of chicken scratch on the waistband, along the top of the pocket, and above the hem. It's exactly the same design I showed above; just repeat to form rows.
To read more about chicken scratch embroidery and to see some different designs check out:
A Feeling Stitchy post on Chicken Scratch.
LindaB's Flickr set with beautiful examples from her vintage apron collection.
General instructions including a pattern for a heart-shaped motif.
Some background and a pattern for an eight-pointed star.