Supernumeray B chromosomes (Bs) are optional additions to the basic set of A chromosomes (As), and occur in all eukaryotic phyla. They differ from the basic complement in morphology, pairing behaviour, and inheritance, and are not required for the normal growth and development. The current view is that Bs are parasitic elements, and comparable to selfish DNA like transposable elements. In contrast to transposons Bs are autonomously inherited, independently of the host genome, and have their own mechanisms of mitotic or meiotic drive, contingent upon the species concerned. Although Bs were described first a century ago, little is known about their origin and molecular make-up. The widely accepted view is that they are derived from fragments of As and/or generated in response to interspecific hybridisation. Here we show that B chromosomes of rye are unexpectedly rich in gene-derived sequences, which allowed us to trace their origin to fragments of several of the As with the largest parts corresponding to chromosomes 3R and 7R. Compared to As, B chromosomes were also found to accumulate large amounts of specific repeats and insertions of organellar DNA. The origin of rye Bs was estimated to about 1.1-1.3 million years (MY) ago, thus overlapping in time with the onset of the genus Secale (1.7 MY ago). We propose the first comprehensive model of B chromosome evolution, including its origin by recombination of several A chromosomes followed by capturing of additional A-derived and organellar sequences and amplification of B-specific repeats.