The HBO pilot, penned by The Thick Of It writer Armando Iannucci, stars Julia Louis-Dreyfus as a former senator who becomes the vice-president.
According to Deadline, Chlumsky has joined the show as Amy.
The character, who is the vice-president's chief of staff, has been described as "responsible" but "insecure".
Chlumsky has previously appeared in television shows including Covert Affairs, Law & Order, Cupid and 30 Rock. She also had a role in Iannucci's movie In The Loop.