The spaceship, called Endurance, will dock with the ISS at 7:10 pm Thursday (0010 GMT Friday), with streaming provided by NASA.
The flight was initially set for Halloween but postponed first for weather, then a "minor medical issue" affecting one of the crew. NASA did not say who it was but said it was not Covid-related.
Chari, a US Air Force colonel, is commanding the mission and making his first trip to space, along with Barron and Maurer.
Marshburn, a medical doctor, flew aboard a Space Shuttle in 2009 and a Russian Soyuz spacecraft in a mission from 2012-13.
Barron, who along with Chari was selected for the NASA astronaut corps in 2017, the most recent recruitment, previously served as a submarine warfare officer for the Navy, while Maurer, a materials science engineer, will become the 12th German in the cosmos.
Crew-3 is part of NASA's multibillion-dollar partnership with SpaceX that it signed after ending the Space Shuttle program in 2011 and aims to restore US capacity to carry out human spaceflight.
The quartet will spend six months on the orbital outpost and conduct research to help inform future deep space exploration and benefit life on Earth.
Scientific highlights of the mission include an experiment to grow plants in space without soil or other growth media, and another to build optical fibers in microgravity, which prior research has suggested will be superior in quality to those made on Earth.
The Crew-3 astronauts will also conduct spacewalks to complete an upgrade of the station's solar panels and will be present for two tourism missions, including Japanese visitors aboard a Russian Soyuz spacecraft at the end of the year and the Space-X Axiom crew, set for launch in February 2022.
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© 2021 AFP