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Jay Z pulled out all the stops Tuesday night during J. Cole's b-day concert in NYC -- surprising the 29-year-old rapper with an incredible guest performance ... before handing over a priceless piece of rap history.

The crowd went WILD at the Garden -- Hov came on stage and performed "PSA" while J.Cole stood in shock ... it was awesome.

But the best moment by far was when the music stopped ... Jay Z pointed at the diamond chain around J. Cole's neck -- Jay Z's original Roc-A-Fella chain from when he founded the label in the 90s.

J. Cole thought he was wearing the chain on loan for the night ... but Jay Z turned to him and said, "That, on your neck, is my original Roc chain -- and it's yours."