We perform single-molecule partitioning measurements of the free energy of chain confinement and self-exclusion as a function of Confinement dimension and buffer ionic strength via single-molecule Tetris. Individual DNA chains, confined in a nanoslit with a lattice of embedded nanocavities, partition their contour between the cavities. Changes in device geometry and buffet chemistry lead to changes in the number of cavities occupied. We are able to deduce the confinement free energy difference between the nanocavities and the nanoslit by observing how the number of cavities occupied by a single chain varies as a function of device dimension. These measurements enable us to confirm theoretical predictions for confinement free energy based on worm-like chain formalism and quantify the chain effective width w, providing a direct measure of the size of excluded-volume effect on a single-chain level.