The fertile offspring criterion is problematic because of the ring species mentioned above, but also due to habitat considerations. Individuals from different populations might be able to produce fertile offspring, but still be incapable of surviving in each other's natural habitats.
From example, polar and grizzly bears can produce viable and fertile offspring, but a polar bear could not survive in the natural habitat of a grizzly, nor could the latter in that of the former. Do they still belong to the same species? The fertile offspring criterion says they do, but is that really a useful definition if you cannot substitute one for the other?
You might be content to dismiss these issues as minor, and to accept the criterion in light of the many cases for which it is useful, but what about species that do not reproduce sexually? For those, it is utterly useless. Genetic thresholds are tempting, but any such threshold would have to be arbitrary, and could not possibly be universal, for different kinds of organisms exhibit very different amounts of genetic variability. Humans have more than 98% of common DNA with bonobos, yet they are universally considered to be different species. However, known strains of E. coli have less than 40% of common genetic material, and are nevertheless deemed a single species.
After carefully pondering these semantic issues, studying known phenotypic data about the Gallus genus, and extensively comparing its recorded genome, transcriptome and proteome, I have come to the conclusion that what came first were neither chickens nor eggs, but McNuggets.