LaGold sent me a PM, asking me to identify the button.
It is the front of a 3-piece KMI (Kentucky Military Institute) Cadet button. The initials KMI are on its front, below the eagle. A non-excavated complete one is shown in the Albert button-book in the Schools-&-Universities section as button SU-193. That version of KMI button dates from slightly before the civil war through several decades afterward. Due to LaGold's find lacking its back, it cannot be accurately dated to a particular point within that wide timerange. However, if civil war Military relics have been dug very-nearby, it is probably civil war era.
About its rarity:
Civil war ones are scarce, but no longer considered super-rare, because about 25 years ago some diggers got onto the KMI campus and dug hundreds of them, with backmarks from both before and after the civil war. Yours is still a rare one, because it did not come from the KMI campus.