The body of a 20-year-old man was discovered in a flat in Usher's Court, Trowbridge on Monday evening.
Police believe there is no suspicious circumstances surrounding the death.
Formal identification has not yet taken place, but is expected to happen in due course.
A spokesman for Wiltshire Police said: "Our thoughts are with the man's friends and family at this difficult time."
Reporter - Amy Pantall WILTSHIRE TIMES