According to the Oxford English Dictionary, the use of the word “property” in the theatrical sense first appeared around 1425 A.D. In the prologue to the play, The Castle of Perseverance, the second flag-bearer announces to the audience:
Grace, if God wyl graunte us, of hys mykyl myth,
þese parcellis in propyrtes we purpose us to playe
þis day seuenenyt
This transcription comes from The Macro Plays, edited by Frederick James Furnivall and Alfred William Pollard, published in 1904. You can see the original manuscript below:
In a modern translation offered by Alexandra F. Johnston, we have:
Grace, if God will grant us of his great might,
On scaffolds with costumes the roles we will play
This day sevennight
While certainly clearer in meaning, this translation has the unfortunate side effect of replacing “properties” with “costumes”, thus nullifying the Oxford English Dictionaries assertion of the word’s first appearance. Still, I think we can give the OED a little more scholarly weight in this instance.
According to Wikipedia, The Castle of Perseverance is not only the earliest known full-length vernacular play in existence, it is also important for its inclusion of a set drawing. The drawing is also one of the earliest known surviving examples of its kind. It hints that the play may have been performed in the round.