The self-assembly of cylinder-forming block copolymer (BCP) microdomains confined within chemical stripe patterns of widths incommensurate with the natural period of the copolymers, L0, is studied. It is shown that this incommensurability causes changes in both the shapes of the microdomains and their spatial period. Specifically, a transition from n to n + 1 rows of microdomains is observed when the stripe width is about n ± 1/2 L0. When the stripe's width is comparable to L0, ellipticity of microdomains can be induced with an aspect ratio up to 2.2. Free energy models are applied to describe the energetic origin of such behavior. Although our observations qualitatively resemble results in sphere-forming BCPs confined in topographical trenches, the quantitative difference is noteworthy and technologically important for the design of nanostructures with programmable shapes.