I don't have that machine, but it sounds to me as if the top tension is way too tight. This will cause the material to gather (because the upper thread is shorter than the fabric); when you cut between the pieces and smooth out the fabric, the top thread is shorter than the fabric. If you leave lots of thread between pieces, then when you smooth you will have enough top thread for the fabric. It would be a lot easier to simply loosen your upper tension, though.
Edit: I just want to mention that I had to read your post carefully because you said "chain stitch". This is a specific kind of stitch that most domestic sewing machines don't make. I think what you meant to say was "chain piece", which is what most of us quilters do a lot of.
Edit2: When you smooth out the fabric, see if it is the top thread that is too short. In this case, after smoothing, you will have a long loose bobbin thread but a much shorter top thread.