I've often found the claim that "Chomsky's views are dominant in current linguistics". Beyond the merits and demerits of Chomsky's proposal, I'd like to focus just on the sociological aspect of this claim: is there any empirical data about trends in current linguists's opinions, or about trends in current linguistics's publications, that could support or refute this claim?

I am unsure of Chomsky's current status among linguists but I doubt the existence of such a poll. I know that Steven Pinker generally agrees with Chomsky on the existence of an innate grammar but that would be the extent of my knowledge of modern linguistics. Chomsky asserts that language acquisition is a social activity but we have a priori structures (innate or universal grammar) that exist in the human mind facilitating the human ability to learn language. Chomsky uses an intuitive example to express his point: lets say we have a household with two parents, a dog and a baby. The baby and the dog (both incapable of speech) are exposed to the same social environment yet one eventually learns language (the baby) and the other does not (the dog). To Chomsky, this is evidence of an innate grammar that is unique to the human mind(also I feel I should point out that Ludwig Wittgenstein used this very example before Chomsky was old enough to talk). Steven Pinker generally agrees with this observation but he expands upon it by asserting that specific structures in the brain have evolved via natural selection to process, learn and perform language.

I feel that Chomsky is generally dismissed as a rationalist (by that I mean a Cartesian rationalist not "someone who is rational") by some but I think this criticism is only partially true. Chomsky does assert the existence of an innate grammar he accepts that language is a social phenomena and is learned through experience. For instance, a feral child raised by wolves does indeed possess an innate grammar yet the child would not in this circumstance acquire language because he/she did not grow up in a social environment that effectively cultivated this innate grammar.

In conclusion, I think Chomsky's work is fairly influential but I don't know if I would go so far as to say "dominant". He asked some interesting questions that steered the linguistic community in various directions but there are still many linguists who disagree with his UG theory; George Lakoff comes to mind.

To Chomsky, this is evidence of an innate grammar that is unique to the human mind(also I feel I should point out that Ludwig Wittgenstein used this very example before Chomsky was old enough to talk). Steven Pinker generally agrees with this observation but he expands upon it by asserting that specific structures in the brain have evolved via natural selection to process, learn and perform language

Ideas about the innateness of language go further back than Wittgenstein to rationalist and idealist philosophy such as that of Kant and von Humboldt. I'm not sure what you mean by when you say it's an expansion to assert that specific language structures in the brain have evolved via natural selection, when that's true of any biological system.

For a good overview of the effect of Chomsky on linguistics over the years, I would reccomend "The First Word" by Christine Kenneally. Altough not specifically about Chomsky or Chomskian linguistics, it gives a broad overview of the rise of Chomskian views of language following his savaging of the behaviousrism of Skinner, and then goes on to detail the subsequent backlash by other linguists and giving views from various other disciplines connected to linguistics.
One of the problems about trying to deal with Chomsky is that he has changed his mind quite often, but as Kenneally points out, this usually takes the form of saying that his critics have not fully understood what he meant the first time round. He is not known as being the most gracious of academics.
On a personal level, I have occasionally come across poor English language majors in Japan ploughing their way through generative grammar and trying to draw those word trees.
Maybe I'm just not smart enough to understand it, but in terms of langauge teaching, drawing word trees always struck me as being like teaching people how to do maths by training them to represent numbers with bar codes. Yeah, you can think of it in those terms, but it's not the way most people think about numbers.
(Ok, fair enough, Chomskian linguistics never claimed to be about L2 learning, but you get my point.)

Interesting article here about Chomsky's views on language and child language acquisition.

http://www.scientificamerican.com/article/evidence-rebuts-chomsky-s-theory-of-language-learning/

No only does it look as if the good professor has been wrong all these years, the article also gives some insight into how theories can be proposed and then gather a following and then hold on long after they should have been discarded.