The phenomenon of crossing-over is analyzed and qualitatively described, from the point of view of quantum mechanics, in the case where the chromosome consists of a single molecule of DNA. First, it is shown that the configuration in which two identical molecules of DNA are lined-up side by side for their entire length, with similar base-pairs closeto each other, is one of minimum energy and tends to occur spontaneously as a result of thermal motion. Next, a model is proposed which depicts crossing-over as a process in which a resonance transfer between two identical bonds from the sugar-phosphate backbones of two corresponding helices occurs, followed by a rotation of the two molecules due to thermal collisions and by a second resonance transfer between the same bonds of the other two helices.