When I get to the chine I pare the existing strips back so the new edge aligns with the chine. This allows the next strip to fit easily on the far side of the chine angle.
Before doing this I made sure I had strips completely covering the side below the chine. Since the chine is not parallel to the strips, some of the strips don't need to be full length to extend above the chine line. Once I had completely stripped up past the chine line, I could then trim back to the intended line without leaving gaps.
When the chine line has been trimmed I then proceed again with full length strips.