Closed feather stitch
This stitch is very similar to double chain stitch: for double chain, the loop of the chain is taken down inside the loop of the previous chain; for closed feather, the needle is taken down just outside the previous loop.
N.B. Historic references to closed or close feather stitch may be referring to long and short stitch (feather stitch is an alternative name), rather than this stitch.
Structure of stitch
Mrs Archibald Christie, Samplers and Stitches (1921) , p.31–2
Mary Thomas, Mary Thomas’s Dictionary of Embroidery Stitches (1934) , p.93
Jennifer Campbell, Ann-Marie Bakewell, Guide to Embroidery Stitches (2004)
Sarah Whittle, The Needlecraft Stitch Directory (2012)