From Nature:
Researchers delving into the DNA of Neanderthal remains have found the human form of a gene crucial for the development of language.
The result indicates that this modern form of the gene could have appeared much earlier than previously thought — in the ancestors of humans and Neanderthals. However, the presence of this gene alone does not guarantee that Neanderthals actually spoke to each other using anything that we would classify as a language. Studies of their anatomy haven’t answered this question either: a bone in the Neanderthal throat called the hyoid resembles the human form, but the inner ear appears different.
More here.