"I think there's more to this Hobbit than meets the eye," Gandalf said.
There was a hushed – nearly reverent – silence as Frodo revealed his precious armor, then Legolas laughed.
"What is it?" Frodo asked.
The Elf smiled. "It just strikes me that a coat of armor made to be the plaything of an Elven princeling should save the Ringbearer's life. When the dragon came to Erebor, when I was a child, I was most distraught that I would never get to wear my mithril coat. But it is so much better this way than had I owned it."
"So it belongs to you!" cried Frodo, jumping to his feet.
Legolas held up a hand. "It was made for me, but it belongs to you. An it's not as if I could fit into it now. If you must, think of it as my gift to you. It will serve you well – certainly far better than our swords and bows ever could, though not from lack of trying on our part."
Frodo grinned sheepishly. "Thank you, Legolas."
Boromir coughed. "The orcs," he reminded everyone, and they galvanized into action.
….oOo….
"Mr. Baggins!" [Thorin] cried. "Here is the first payment of your reward! Cast off your old coat and put on this!"
With that, he put on Bilbo a small coat of mail, wrought for some young elf-prince long ago. It was of silver-steel, which the elves call mithril, and with it went a belt of pearls and crystals.
The Hobbit, by J.R.R. Tolkien, Chapter XIII: Not at Home
….oOo….
***Smaug descended on Dale 348 years before the events in The Lord of the Rings, according to "Appendix B" of The Return of the King, and Legolas is the only Elf-prince that we know of who was alive at that time. I don't think it's too far of a stretch for the mithril coat to have been made for him, but if it is for you, then please consider this AU.