Her finding is especially significant as it shows that chewing gum existed even 5,000 years ago.
The lump of birch-bark tar, complete with visible tooth marks, has now been sent for analysis where it is expected to be carbon dated at around 3000BC.
"I had heard of ancient chewing gum being found before on previous European digs so when I found it in the trench, it was the first thing that crossed my mind," the Scotsman quoted Pickin, as saying.
"However, it looks just like a dirty piece of modern chewing gum with no smell or taste and I was also worried it could have been a bit of fossilised poo, so I asked a few of the other students to make sure.
"Thankfully they agreed that it was birch-bark gum and it's now away to be carbon dated and have the teeth marks analysed before it goes on display," she added.
Pickin's tutor at Derby, Professor Trevor Brown, a heritage and conservation expert, said: "Birch-bark tar contains phenols, which are antiseptic compounds.
"It is generally believed that Neolithic people suffering from gum infections found that chewing this stuff helped to treat the condition.
"The actual material is some kind of tar, which was made by heating the birch bark. After the tar was made, it was boiled, and when it cooled, it became solid. When it was heated again, it became softer, and only then was it used as a kind of chewing gum. Sarah's discovery is particularly significant because well-defined tooth imprints were found on the gum."
Pickin's discovery has helped her make up her mind to study the history of the chewing gum further.
"I was delighted to find the gum and was very excited to learn more about the history of it," she said.
"I'm keen to work in this area in the future and I'd love to go back to the site, so I'm hoping they're impressed by the gum and the tests come up with some interesting results," she added.