Back-stitched chain stitch
This stitch is, as its name suggests, a combination of back stitch and chain stitch. Having stitched a line of chain stitch, a line of back stitch is then stitched over the top: each stitch starts and ends in the centre of each loop of chain.
For more background see the entries for back stitch and chain stitch.
Complete a row of chain stitch.
After completing a row of chain stitch, work a back stitch over the top by bringing the needle and thread up in the centre of the second loop of chain,
and taking the needle down in the centre of the first loop of chain. A straight stitch should lie over the intersection of the chain.
Bring the needle up again in the centre of the third loop of chain
and back down into the second chain to meet the previous back stitch by sharing the same hole.
Continue to cover each chain intersection with back stitch.
Mrs Archibald Christie, Samplers and Stitches (1921) , p.42