Are you saying the center square is 1/8" larger? That's such a small amount, I think you'd be fine to just center the square against the first log. If they are all 1/8" off, make sure that when you hold your ruler over the sections of fabric to cut, that the line is directly on or even just butted up against the edge of fabric.
I would make a test block...just enough to make one. Figure out your hiccups now before you cut out all those blocks. Chain piecing is exactly how I'd make this too...and I've been quilting for ten years.
