If you are referring to a "chord" as being a triad, ie, 3 (or more)notes which are purposely played simultaneously to bring about harmony, The oldest "chord" was possibly played on an ancient harp--the first known stringed instrument. If you allow for 2 notes being enough to constitute a chord, then most likely in was in the earliest know song: on clay tablets circa @ 4000 years old, found in Ugarity, Syria, & Prof. Anne Draffkorn Kilmer deciphered the writing, and bellieves she has found the first written song, which shows a melody & a harmony part which is a third lower (most of the time). If your definition expands to include any & all musical instruments, voices were most likely to have produced a "chord."