The Tarkannans were a species native to the Alpha or Beta Quadrant, that made first contact with the Federation in the late 2340s.
On Chakotay's first posting, his ship was sent to make first contact with them. He studied up on all the information they had on the Tarkannans, and pestered the captain to let him be on the diplomatic team. When he finally came face to face with their delegation, he very proudly made the traditional gesture for "hello", not realizing that males and females of their race use different styles of movement. He later found out that he had actually propositioned the ambassador.
While making first contact with the Drayans in 2372, he was reminded of this encounter, and explained it to Captain Janeway. (VOY: "Innocence")