Before Downsizing, she appeared in the television series Treme (2010–2013) and the film Inherent Vice (2014). In 2018, she had guest star roles in several TV series. In 2019, she played a supporting role in the limited series Watchmen, and had leading roles in the films American Woman and Driveways. In 2020, she had a starring role in the second season of the TV series Homecoming, having had a supporting role in its first season in 2018. In 2022, she appeared in supporting roles in the films Showing Up, The Menu, and The Whale with the latter earning her a nomination for an Academy Award for Best Supporting Actress.
Chau was born to Vietnamese parents who lived in a refugee camp in Thailand after fleeing Vietnam in the late 1970s. A Vietnamese Catholic church in New Orleans, Louisiana sponsored Chau and her family to move to the United States. She grew up in New Orleans and studied film at Boston University before pursuing an acting career.