It has long been conjectured that the canonical genetic code evolved from a simpler primordial form that encoded fewer amino acids [e.g., Crick, F. H. C. (1968) J. Mol. Biol. 38, 367-379]. The most influential form of this idea, "code coevolution" [Wong, J. T.-F. (1975) Proc. Natl. Acad. Sci. USA 72, 1909-1912], proposes that the genetic code coevolved with the invention of biosynthetic pathways for new amino acids. It further proposes that a comparison of modern codon assignments with the conserved metabolic pathways of amino acid biosynthesis can inform us about this history of code expansion. Here we re-examine the biochemical basis of this theory to test the validity of its statistical support. We show that the theory's definition of "precursor-product" amino acid pairs is unjustified biochemically because it requires the energetically unfavorable reversal of steps in extant metabolic pathways to achieve desired relationships. In addition, the theory neglects important biochemical constraints when calculating the probability that chance could assign precursor-product amino acids to contiguous codons. A conservative correction for these errors reveals a surprisingly high 23% probability that apparent patterns within the code are caused purely by chance. Finally, even this figure rests on post hoc assumptions about primordial codon assignments, without which the probability rises to 62% that chance alone could explain the precursor-product pairings found within the code. Thus we conclude that coevolution theory cannot adequately explain the structure of the genetic code.