Cincinnati was anointed capital to replace DC. Maybe the Confederates burn down Washington and the US relocates the capital to a more safe position for the duration of the war. Post-War Lincoln never returns to Washington and the capital remains in Chicago.
They might move the capital to signify a break with the old bourgeoisie goverment and a new era in history. They might select Chicago because it is a large, industrial city, but one that is more central in the US, and it doesn't have any historical connetations with the ousted goverment.