The interphase nucleus of the human eukaryotic cell, before DNA replication, contains 46 linear DNA molecules, each of the order of centimeters in length, in a spherical nucleus with a diameter of 3-10 microns. How does the cell avoid topological entanglements between the 92 linear DNA molecules following replication? A model of chromosome replication is introduced, based on the assumption of the existence of a physical linkage between diverging growing forks during eukaryotic chromosome replication. This basic model is shown to be sufficient for the avoidance of DNA duplex entanglements during DNA replication. The model also suggests structural characteristics of chromosomes at various points in the cell cycle and provides a possible partial mechanism for chromosome condensation at the end of replication.