Is a letter a primary source?

It depends on the circumstances of the letter and the historical event under investigation. A primary source is anything produced at the time and place of the historical event under investigation. To give an example of how the same letter may be a primary or a secondary source, let's presume that a letter was written by an American woman, who is a Professor, to her friend in 1922 about the Ancient Athenian government system. If the 'event' under study is the Ancient Athenian government system, then this letter is a secondary source since it was not produced at that time and place. However, if the study is modern women's interpretation of Ancient Greek politics or if it is a biography of this female Professor then it is a primary source since it is produced at the time and place of the event.