The Adamic language, according to Jewish tradition (as recorded in the midrashim) and some Christians, is the language spoken by Adam (and possibly Eve) in the Garden of Eden. It is variously interpreted as either the language used by God to address Adam (the divine language), or the language invented by Adam with which he named all things (including Eve).
Scholars are not certain as to whether or not the Adamic language was Hebrew, due to the names he gave Eve. We do know that Adam used his language to name Eve. It is prudent to note at this point that his female companion was not originally called Eve. The scripture was not in English, and she was in fact called Isha or Chava. As these names apparently only make sense in Hebrew, some assume that this was the language Adam was speaking.
The scriptures state that this language, written and spoken by Adam and his children, was "pure and undefiled". It is said that it continued from Adam to Babel, at which time the Lord "caused the people to forget their own mother tongue;scatter[ing] them abroad upon the face of the whole earth," except possibly for Jared and his family in the Book of Mormon.