Chester, who took over from James Allison as technical director at the Enstone team in 2013 when it was known as Lotus, remained in charge of the squad's technical operations until 2020.
Thereafter, he joined the Mercedes Formula E squad where he was part of the team's back-to-back drivers' titles in 2020-21 and 2021-22, and remained there for its initial transition to McLaren.
In Andretti's hunt for F1 experience, a source has confirmed to Motorsport.com that the team has managed to lure Chester from Formula E to head up its technical operations as it continues its expansion plans.
The American squad has, after a period of making its plans to join F1 known publicly, submitted its official expression of interest to join the field to the FIA as the governing body opened the application process for as early as 2025.
However, Andretti's declaration of interest has earned cool reactions from the current cast of F1 teams, with them attempting to cement their franchise value by pushing the entry fee up from $200m to $600m.
To bolster its chances of securing an entry, Andretti has linked up with General Motors to introduce the Cadillac brand into F1, although this would not involve the American marque producing its own powertrain.
The team's facilities in Indiana are in the process of being expanded as Andretti continues to diversify its motorsport interests, while the team is currently hiring engineers for positions in Banbury – suggesting that the Formula E facility in the Oxfordshire town will also house part of the F1 team.
Andretti has been approached for comment on Chester's signing, but Motorsport.com has currently received no response.
The Briton started in F1 with Simtek in 1994 before moving to Arrows in 1995, later becoming the engineer for Damon Hill in 1997 before working with Mika Salo and Pedro de la Rosa.
He then moved to Benetton in 2000 to join its test team, staying with the Enstone outfit through its various guises for almost 20 years.
In the meantime, McLaren has recently signed Chris Dyer, Michael Schumacher's race engineer at Ferrari during many of his F1 title-winning years, from Alpine to bolster its Formula E and Extreme E technical departments.
