Chromosomes are not distributed randomly in nuclei. Appropriate positioning can activate (or repress) genes by bringing them closer to active (or inactive) compartments like euchromatin (or heterochromatin), and this is usually assumed to be driven by specific local forces (e.g., involving H bonds between nucleosomes or between nucleosomes and the lamina). Using Monte Carlo simulations, we demonstrate that nonspecific (entropic) forces acting alone are sufficient to position and shape self-avoiding polymers within a confining sphere in the ways seen in nuclei. We suggest that they can drive long flexible polymers (representing gene-rich chromosomes) to the interior, compact/thick ones (and heterochromatin) to the periphery, looped (but not linear) ones into appropriately shaped (ellipsoidal) territories, and polymers with large terminal beads (representing centromeric heterochromatin) into peripheral chromocenters. Flexible polymers tend to intermingle less than others, which is in accord with observations that gene-dense (and so flexible) chromosomes make poor translocation partners. Thus, entropic forces probably participate in the self-organization of chromosomes within nuclei.