Chase was born in Australia in 1979. His father was Rowan Chase, who later became a wealthy and world renowned rheumatologist. Rowan had emigrated to Australia from Czechoslovakia a few years before Robert was born. The name of Chase‘s mother has never been revealed. It is presumed Robert has other siblings (most likely half or step-siblings), but their names have never been revealed. However in "Better Half," he reveals that he has a younger sister who he took care of. He also commented that she "ended up drinking half her life away and hating me," but he did call her at the end of the episode.
However, Chase had a rough relationship with both his absent father and alcoholic mother. When Chase's father left the family, 15 year old Chase was forced to care for his mother until her death which is approximately ten years before Season 1. Dealing with his mother helped him empathize with Luke Palmeiro, another teenager who was trying to deal with a parent who couldn't care for herself.
With what appears to be a total lack of parental supervision during his adolescence, Chase admits to having wild teenage years and experimented with drugs and sex. However, his father continued to support the family excessively (probably out of guilt). Despite the enmity between them, Rowan never failed to come through for Robert when he needed something, even if it was only an expensive vacation. Even when Robert started working at Princeton-Plainsboro, it was clear his father was financing his lifestyle because Robert, unlike the other fellows, never cared about money.
Chase was raised a Roman Catholic, and although he is no longer observant, he still considers himself religious. In Damned If You Do, Chase reveals to a patient that he attended a seminary after graduating high school, quoting 1 Peter 1:7. In The Tyrant, he revealed that he took his seminary training in England. This aspect of his life was shown again in the episode Forever, when he said a prayer for the soul of a baby who died under his care.
However, Chase had a crisis of faith (if one can call sleeping with the groundskeeper's wife a "crisis of faith") while in the seminary and realized that it wasn’t for him. Instead, he went to medical school doing his pre-medical studies at the University of Sydney (as revealed in Season 7). He does not appear to have been an outstanding student. However, his later training was outstanding. As well as completing specialties in intensive care and cardiology, he also took a residency in neurosurgery at Melbourne Hospital, although he never became a board certified neurosurgeon.
Before the Series
Chase was the longest serving fellow at the start of the series, having been on the team since 2002. It appears he was interested in the job and asked his father to see what he could do. House admits that he hired Chase after Rowan called him, but has never made his reasons clear. It turns out that Chase beat out another doctor who had moved to Princeton in an attempt to get the job, Dr. Peter Treiber.