A recent paper in the proceedings of the Royal Society there is a paper by Collier, Bickel, van Schaik, Manser and Townsend (CBvSMT) (here (and a little discussion here)) that tries to address the question: what came first, phonology or syntax. Chomsky has recently focused attention on this kind of question by noting that there are evolutionary arguments for divorcing the structure of language from its use in communication. Those interested in this topic and his views on this can go to the first of his lectures, where he develops this theme at length (see here and here). At any rate, the paper linked to above develops this theme from another direction. The "syntax" discussed is very rudimentary. However, there is an interesting observation that the paper makes. It argues that there is not much phonology in the vocalization systems of other species. There are vocal patterns, but nothing like a system of sounds that serves to differentiate different meanings. If phonology is taken to be at the service of building hefty lexicons systematically, then it seems that very few vocalizers have phonology in this sense. In fact, as they put it, the capacity to form various phonetic patterns is not sufficient to develop a phonology OR a syntax. The suggestion in the paper is that phonology only becomes worth developing once a syntax is there to support compositionally (viz. the capacity to combine smaller meaningful parts into larger ones). Once this capacity is there, the cash value of phonology and its capacity to support a large lexicon comes into play. Indeed, CBvSMT here even suggests that phonology is akin to the way Dehaene views reading (here); a capacity to use articulatory hardware for phonological purposes, much as the visual system and auditory system can combine to give us letters and reading. Here's what the authors say:
Like songbirds  and some
mammal species (cetaceans , pinnipeds , elephants
, bats ), humans are vocal learners capable of producing
a large number of different sounds. However humans are, as far
as we know, the only species that use these sounds phonologi-
cally to distinguish between the meanings of two sequences.
This suggests that vocal learning and the capacity to produce a
large number of different sounds alone are not sufficient to
induce the emergence of a phonological level. We therefore
argue that the constraints leading to the use of a phonological
level are more likely to be cognitive in nature rather than
linked to the production capacity of a given species. Specifically,
once humans developed the cognitive capacities to memorize
phonological combinations and their meanings, phonology
itself could become subject to cultural, as opposed to biological, evolutionary processes [23,64]. If this is the case, it might
explain why phonology in the linguistic sense is so rare in the
communication systems of other species.
Truth be told, the "syntax" they point to is very rudimentary. However, the argument form is interesting. CBvSMT notes that there are a lot of animals, many far removed from us in evo time that vocalize but only WE speak. As Paul Pietroski has observed (and I really hope he writes this up), this suggests that vocalization is the sort of thing that is just part and parcel of animal cognition. It's the sort of thing that animals as such can do given the right selective motivations. The availability of syntax would be just that kind of motivation for it would make having a large vocabulary all that more useful. Once one acquires a generalized combinatoric trick, having lots of units to combine (and thus a way of coding such units systematically) really becomes useful. Given that mammals are congenitally able to develop vocalization (as witnessed by the fact that so many different kinds of animals have done so (from reptiles (birds) to mice, to whales to…), the adventitious emergence of syntax would make developing phonology from vocalization a real plus. So, syntax first bringing with it semantic compositionally and then phonology to really crank this capacity up. Or, as Chomsky might put it, language isn't sound and meaning but meaning WITH sound, the second exploiting the opportunities opened up by the first.
So, take a look. Chomsky has identified two traditions regarding the "function" of language (as if it had a function!). The dominant one is that it is a tool for communication. An older tradition thinks of it as a tool for the expression of thought. The first tradition would seem to fit well with the idea that language emerged from vocalization in some way. The second that vocalization is a secondary effect. The CBvSMT paper addresses these issues from an angle different from Chomsky's but comes to similar conclusions. Not every day that we find two different roads to Rome.