Pin the two fleece pieces wrong sides together, placing pins at right angles to the raw edges.
To determine the right side of fleece, gently pull along the cut edge on the fabric crossgrain (direction of most stretch). Fleece will curl toward the wrong side.
Draw a 45 degree angle line for the first row of stitching. Begin the line 3 1/2" from one short end of the scarf. To help keep the rows of stitching parallel, draw multiple guidelines 3" apart (1), or use your machine's quilting guide.
Using thread to match the fabric colors in the needle and bobbin, and a 3.5 mm stitch length, stitch 3/8"-wide parallel rows beginning at the first drawn line. There's no need to secure stitches at the beginning or end of each row as these will be anchored later. Don't be concerned if the edges of the scarf shift a little-they'll be trimmed even.
As you get close to the opposite end of the scarf, stop and count the number of channels between the stitching lines. Finish the rows of stitching accordingly so you have a channel number divisible by 5. Note: Stop stitching at least 4" from the scarf end. The scarf length can vary according to your preference.
Using a rotary cutter and ruler, trim as necessary to neaten the scarf long edges.
Insert a 1/4"-wide cutting strip under the top fleece layer in the first channel. Using a rotary cutter and ruler, carefully slash open down the channel center (2). Repeat until you have slashed five channels.
Turn the scarf over and follow the same procedure, slashing open the next five channels on the opposite side. Repeat this process on alternating scarf sides to slash open all the channels.
Topstitch 1/2" from both long edges to secure the stitching rows and chenille cuts, beginning and ending stitching at the chenille cuts. To keep the slash cuts flat while stitching, place a strip of lightweight tear-away stabilizer on top of and underneath the scarf edges. The slash cuts will naturally lie flat until roughed up to bloom-the stabilizer prevents the feed dogs and/or presser foot from disturbing the chenille cuts while stitching.
Draw a line parallel to and 3 1/4" from the last stitching line at each scarf short end. At each scarf end, trim the scarf on the line and make 1/2"-wide fringe cuts.