This is a non-sequitur because you're implying that such a mutation would be binary: either a creature has it and can communicate with creatures that have the same, or it hasn't and communication is impossible. That's not how evolution works, specialization of organs can happen over thousands of generations. If a specific mutation is beneficial, it spreads through the population over time, and additional mutations in that area can further develop the organ.

Second, our speech apparatus isn't one "organ" in the narrow sense: our lungs/vocal chords/tongue/lips/cheeks/jaw all contribute to the richness of our speech. The breadth of our speaking ability is a specialization of fine muscle control in all those areas, coupled with a finely-tuned hearing apparatus to analyze and understand those sounds.

It doesn't seem like an extraordinary claim to me that our evolutionary path has enhanced our communication ability far beyond our peer species -- because it's clear to see how a rich vocubulary can aid a species' survival over time. I have no knowledge of Chomsky's specific claims, but I don't think you are representing his theory accurately.