Rowan Chase is the father of Robert Chase. He appears to be from a wealthy Australian family (probably of Czech descent; in the episode "Cursed," House speculated that his accent is "Czech with about 30 years Aussie," which he confirms; Jesse Spencer is Australian himself), and Robert has also had a rough relationship with his father, Rowan, a famous doctor in his own right, as Chase talks to House about trying to mend the gap with his father many times, but finding his father simply didn't care.
Eventually, Rowan Chase is revealed to have left the family when Robert was a teenager, which gave his son no other option but to care alone for his alcoholic mother until her death, a good five years later which was approximately ten years before "Damned If You Do". It was later revealed that Chase was also required to care for his baby sister as well. In "Cursed," Rowan visits the hospital claiming he is in town for a medical conference. House attempts to verify the assertion and discovers that Rowan had not registered for it. House also realized Rowan was on a macrobiotic diet and on radiation therapy. With this information, House is able to get Rowan to admit that he was, in fact, dying from terminal (Stage 4) lung cancer. Rowan was at the hospital to visit Dr. James Wilson, an oncologist. Wilson told him he had approximately 3 months to live. Initially, Robert is intensely frustrated with his father's presence, but offers to buy his father a drink at the end of the episode. Rowan declines due to time constraints, and leaves without ever revealing to Robert his condition. The two share an embrace. In the Season Two episode The Mistake, the audience learns that Rowan died about two months after the visit in "Cursed" with the news leaving Chase so devastated that he winds up accidentally killing a patient the team had been treating.
It is suggested in The Mistake that Rowan re-married after leaving Chase's mother, as Chase received the call about Rowan's death from his "stepmother".
Robert Chase has also hinted in the second season that he is now no longer well-off, since he had started working in NICU while taking his paid vacation time in House's department, receiving twice his usual salary. Upon learning that Chase has been putting in extra hours, House speculates that Robert must have been cut out of his inheritance after his father's death and he neither confirms nor denies this hypothesis. However, in the Season Three episode "Finding Judas," he admits that his father left him out of his will, and that he harbors ill will towards Rowan once more.