This stitch, as the name suggests, is a series of chain stitch loops made over rows of straight stitches. It has a raised effect and used in embroidery types like Stumpwork. It looks nice if contrasting threads are used, and it makes nice border stitch. It can also be used as a rich filling stitch by doing multiple rows of chain stitches over a broad row of straight stitches. For demonstration sake, I will be doing only one row of chain stitch over a narrow foundation of straight stitches.

To do this, knowledge of the chain stitch is good, but not necessary. I will use two parallel stitch lines to lay the foundation of the straight stitches. Then, I will be using a contrasting thread to work the chain stitch over it. Remember that we do not go through the fabric or even pluck it when doing the chain stitch as they will be done over the foundation of straight stitches.

raised_chain_band_1   raised_chain_band_2
Fig 1: We first lay the foundation by doing a row of straight stitches. For that, we drive the needle from A-B, C-D, E-F and so on between the parallel stitch lines.   Fig 2: Now, take a contrasting thread and bring it out from the top of the first straight stitch, as shown.
Then, take the needle from beneath the first straight stitch as if to whip it once, as shown. Do not pluck the fabric below. The slant of the needle should be towards the left as shown. 
raised_chain_band_3        raised_chain_band_4
Fig 3: Once you pull the needle out, you will find a tiny loop or ‘whip’ around the straight stitch.
Now, take the needle again from beneath the first straight stitch, but this time from the top right side. Again, do not pluck the fabric below.
Loop the thread around the needle to make the loop of the chain, as shown.
  Fig 4: Your first chain loop will look like this.
raised_chain_band_5   raised_chain_band_6
Fig 5: Continue this procedure for the rest of the straight stitches till you finish the row.   Fig 6: Yor finished raised chain band would look like this. You can finish off the last loop by anchoring it up as shown.