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|A file picture shows a Pilatus PC-12 single-engined aircraft similar to the one involved in the crash, in which nine people were killed AFP/FELIX KAESTLE|
The victims were from four generations of a family, aged between 7 and 81, according to reports.
Jim Hansen and Kirk Hansen, brothers and founders of health and wellness company Kyani, died in the crash, according to a statement by the firm.
Other victims include Jim Hansen and Kirk Hansen's father, two of Kirk Hansen's sons, as well his two sons-in-law.
Jim Hansen's son and grandson also died in the crash.
According to the New York Times, the family was returning home from a hunting trip when their single-engine turboprop plane crashed shortly after take-off.
The accident happened approximately a mile from the Chamberlain airport, while a winter storm warning was in place, the Federal Aviation Administration (FAA) said.
Among the dead was also the plane's pilot, Brule County state's attorney Theresa Maule Rossow said, adding that a total of 12 people had been on board.
The three survivors had been taken to the hospital in Sioux Falls, she told US media.
The flight left the airport just before noon local time, with a destination of Idaho Falls Regional Airport in the western state of Idaho.
The FAA said investigators were en route to the crash site and that the National Transportation Safety Board (NTSB) would be in charge of the investigation.
The NTSB tweeted that it was "investigating today's crash of Pilatus PC-12 near Chamberlain, SD".
South Dakota is located in the Northern Plains, a region facing blizzard conditions as a storm blows eastward across the United States.
A winter storm warning remains in effect in Brule County until midday Sunday, the National Weather Service said, potentially including blowing snow that "could significantly reduce visibility".
"The men and women of law enforcement, first responders and medical professionals should be commended in their heroic actions to rescue the victims in extreme weather conditions," the state's attorney office said.