The Genesis probe, which left Earth in 2001 to gather particles blown off the Sun, returns its cargo on Wednesday.
The chase begins on Wednesday
It will eject a capsule that will enter Earth's atmosphere at 40,000km/h (24,000mph) before slowing, with the help of a parachute, to fall over the Utah desert.
Hollywood stunt pilots are waiting to snatch the parachute in midair to prevent the capsule hitting the ground.
Scientists hope the particles of solar wind can tell them about the evolution of the Sun and the planets.
Entry into the Earth's atmosphere is timed for 1555GMT (1655BST). It will be another 20 minutes before the capsule has descended to a position where it can be grabbed by a helicopter.
"What a prize Genesis will be," said the mission's principal investigator, Dr Don Burnett.
"Our spacecraft has logged almost 27 months far beyond the Moon's orbit, collecting atoms from the Sun.
"With it, we should be able to say what the Sun is composed of, at a level of precision for planetary science purposes that has never been seen before."
The US space agency (Nasa) says it had no hesitation in calling in the movie helicopter pilots for the important retrieval operation.
Cliff Fleming and Dan Rudert have demonstrated their extraordinary skills in dropping water over forest fires; in addition to the daredevil stunts they have performed in such films as Batman, XXX and The Hulk.
Each man will run a pole and hook from their aircraft and aim to snare the parachute when it gets below at an altitude of 3,000m (10,000ft). If one fails, the other will move in to make the grab.
It will be a test of nerve, too. The men know that if they miss their target, the $264m Genesis mission's precious quarry could be damaged in a hard impact with the desert floor.
Inside the capsule are hexagonal wafers of pure silicon, gold, sapphire, diamond and other materials.
These wafers were hung outside the Genesis probe for more than 800 days, sifting space for charged atoms that had been blown off the Sun.
If the capsule were to descend all the way to the Utah desert floor, some wafers might fracture or break away from their mountings, and this could compromise the research on the solar samples which amount to no more than 10-20 micrograms of material.
"One of the more difficult things for us to do is... put the capsule on a very precise spot and very gently," Dan Rudert told the BBC's Science In Action programme.
"It would defeat the point of us doing a midair recovery if we were to slam it into the ground or drag it across the desert floor."
The return of the Genesis probe will mark the first bits of extraterrestrial matter retrieved from space by human means since the 1970s, when Moon rocks were carried back to Earth by manned US Apollo and unmanned Soviet Luna missions.
And although a midair method of retrieval sounds slightly bizarre it has a precedent in the Cold War when military pilots would capture film canisters ejected from spy satellites.
Once on the ground, the capsule will be taken to a clean room at Nasa's Johnson Space Center in Houston, Texas. There, the samples will be preserved, catalogued and made available to the world scientific community.
THE SOLAR WIND
Consists of electrically charged atoms called ions
Flows past the planets in a constant stream
It is a snapshot of "surface" materials in the Sun
Particles reflect the makeup of the solar nebula
Essentially, other than for the main elements hydrogen and helium, the composition of the Sun is unchanged since the beginning of the Solar System 4.5 billion years ago.
The samples collected by Genesis therefore represent a "fossil record" of the solar nebula, the huge cloud of gas and dust out of which the Sun and the planets formed.
Some of the Genesis material will be despatched to the UK's Open University, which has been involved in the development of the collectors and analytical techniques required for the mission.
The aim is to be as gentle as possible with the wafers
The OU's interests include oxygen and carbon isotope analysis.
"Oxygen, and in particular the ratio of the minor types to the more common type, is absolutely fundamental to our current understanding of how the Solar System formed," Dr Ian Franchi said.
"We really need to know what the initial composition of the Solar System was and we'll get that by measuring the oxygen that came from the solar wind."