Try just knitting three stitches with old and new strand together, so the ends point in opposite directions. Knit those three stitches tightly, to reduce the bulk. Leave a 1/4" tail on the "inside" of the garment, if there is one, to keep the ends from popping out to the outside. If there is no inside of the garment, see if you can leave over an 1/8" tail to keep the ends in place; they should be pretty hidden with chenille.
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