The incident took place on Friday at RAF Weston-on-the-Green, Oxfordshire, near RAF Brize Norton. An investigation into the incident has been launched by the RAF.
The dead serviceperson, believed to be female, has not been named.
A spokesperson for the service said: “We can confirm that a Service Person has died at RAF Weston on the Green.
“Our thoughts are with the family, friends and colleagues at this time.
“The incident is being investigated and it would not be appropriate to comment further at this stage.”
RAF Weston-on-the-Green is frequently used as a landing point for parachutists from RAF Brize Norton.
According to the Oxford Mail the RAF trains parachutists from the army, navy and air force at the facility.
The paper adds RAF Weston-on-the-Green is only manned by the RAF part time.
It is also the home base of the Oxford Gliding Club.
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Shocked members of the public took to social media to express their condolences.
One wrote: “That is very sad news RIP.
“I lost a colleague years ago on his first ever jump it is such a tragedy.”
Another added: “It’s the adventure training parachute centre, it has its own plane there I remember doing jumps from there.”
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A third posted: “That's very sad news.”
A fourth expressed a similar sentiment, writing: “Condolences - lest we forget.”
Two other Twitter users simply wrote RIP [rest in peace] in response to the story, accompanied in one case by a union jack emoji.