Staley's band had recorded seven albums
Fans have been leaving flowers on the steps of the building where 34-year-old Staley lived, and have held a vigil in Seattle.
His death comes eight years after Kurt Cobain, leader of Seattle's best-known rock band Nirvana, killed himself.
Local medical officials said that the cause of Staley's death had yet to be determined.
"It was natural or an overdose - that's the way it was determined by our investigators,'' Seattle police spokesman Duane Fish told the Seattle Post-Intelligencer.
Fear of death
Staley was born in 1967 in Kirkland Washington, just east of Seattle.
They ranked with Nirvana, Pearl Jam and Soundgarden as one of the bands that made Seattle famous in the early 1990s.
They recorded seven albums, including a Billboard number one in 1995.
The band stopped touring in the mid-1990s when Staley went into rehabilitation for heroin use.
The front page of the Alice in Chains website on Sunday read simply: "Rest in peace, Layne. Layne Staley, 1967-2002."
About 200 fans turned out on Saturday for an impromptu vigil at the Seattle Center, leaving flowers and notes, and lighting candles.
Among them was Chad Schuster, a 21-year-old student at the University of Washington.
Despite Staley's problems with drugs, the singer was an inspiration for many, Mr Schuster said.
"He was open about his drug problem and his struggles with life, and I think a lot of people can relate to that."
'Scared of death'
Staley told Rolling Stone magazine that lyrics about heroin use came from his own experience.
"They worked for me for years, and now they're turning against me - and now I'm walking through hell, and this sucks," he said in 1996.
He said that he would never think of committing suicide.
I'm scared of death, especially death by my own hand," he said.
"At the end of the day or at the end of the party, when everyone goes home, you're stuck with yourself."