A double crochet foundation chain, also called a chainless double crochet foundation row, is made in the same way as a single crochet foundation row. An extra chain stitch is added to each double crochet stitch to create a chain stitch into which you can make the next double crochet in the foundation. This technique replaces both the foundation chain and the first row of double crochets in your pattern and can be used as substitute in any pattern that begins in that way.
Yarn over and insert your hook into the third chain from the hook.
Yarn over and pull up a loop. You will now have three loops on your hook.
Yarn over and pull your hook through the first loop only. This creates the chain into which you will make your next stitch. You will still have three loops on your hook.
Make a double crochet stitch as normal. To do this, yarn over and pull your hook through two loops. Yarn over and pull your hook through the two remaining loops. This is your first double crochet stitch. You will have one loop on your hook.
Yarn over and insert your hook into the chain stitch you made before (Step 4).
Yarn over and pull up a loop.
Yarn over and pull the hook through the first loop only to make your next base chain.
Make your next double crochet stitch (yarn over, pull through two loops, yarn over, pull through last two loops).
Repeat until you've made as many double crochet stitches as you need for your pattern.