We propose an order index, φ, which quantifies the notion of "life at the edge of chaos" when applied to genome sequences. It maps genomes to a number from 0 (random and of infinite length) to 1 (fully ordered) and applies regardless of sequence length and base composition. The 786 complete genomic sequences in GenBank were found to have φ values in a very narrow range, 0.037 ± 0.027. We show this implies that genomes are halfway towards being completely random, namely, at the edge of chaos. We argue that this narrow range represents the neighborhood of a fixed-point in the space of sequences, and genomes are driven there by the dynamics of a robust, predominantly neutral evolution process.