Emergency crews were called to a property at Caddon Court in Innerleithen, Peeblesshire, early on Saturday but it is understood that 17-year-old Meighan Boyle was already dead.
Police have described Ms Boyle’s death as “unexplained.”
However, police are believed to be examining the possibility that Ms Boyle, who also used the surname Reid, died as the result of a “recreational” drug related incident.
Detectives were seen removing a number of evidence bags from the property.
Ms Boyle’s family have been too upset to talk about the tragedy.
The teenager’s friends took to social media to pay tribute to her.
Amanda Louise-Kerr, 20, posted on Facebook: “Don’t want to believe what I’m hearing Meighs.
“You were one of the most beautiful girls I knew, with the biggest heart. The angels will look after you. Love you.”
Nicola Forrest wrote: “Rip Meighan Reid such a shame. 17 is no age at all. RIP.”
William Byres, who lives nearby, said Meighan’s death was a “bombshell” for the town. “She as a really nice lassie, she would do anything for anybody.”
Another resident said: “If drugs were involved, it’s even more sad – especially with someone so young.”
Marshall Douglas, chairman of the Innerleithen community council, said that people in the close-knit community were extremely upset by the tragic incident.
“I was very saddened by the news. My thoughts go out to Meighan’s family and friends at this time.
“It is very distressing to hear that someone has died at such a young age, robbed of all the potential they had for living their life to the full.
Mr Douglas added: “In a small town like Innerleithen a lot of people know each other and this is bound to affect many people.”
A Police Scotland spokesman said: “Police in the Scottish Borders are investigating following the death of a 17-year-old woman at an address in Innerleithen.
“The woman’s body was discovered on Saturday 18 November. The death is being treated as unexplained, however the circumstances are not believed to be suspicious. A report will be submitted to the procurator fiscal.”