The stick -- one of the first-ever made -- is believed to be from the time period between 1850 and 1870 ... as the game of hockey was being invented.

Here's the deal ... in 1980, a couple -- Gary and Germaine Morse -- discovered the one-of-a-kind stick sitting in the closet of a Vermont home they recently purchased.

The Morse's had no idea what the stick was worth ... so they had it assessed.

The value, according to the expert fine art appraiser?

3.5 MILLION DOLLARS!!

Shockingly, they held on to the stick for 40 years -- until recently deciding to cash out -- going to Goldin Auctions and asking them to unload the piece.

We know, sounds like a helluva lot of money for a very old piece of wood ... but 100+-year-old sticks have a track record of selling for a fortune.

The "Rutherford Stick" -- also believed to be from the 1850s -- reportedly sold for $2.2 million in the mid-2000s.

Question is, what will a similarly old and rare stick go for at auction?

We'll know soon ... bidding kicks off on Friday.