robert chase really has an issue with talking to people, especially people he dosen't know.
the two jobs we see him have outside of working for house are in the NICU and as a surgeon. what links both of those departments? you don't have to talk to the patients.
it's also rare he tells anyone, even his closest friends, about his life and his past. before the episode 'cursed' (s1, e13), chase had worked with house for roughly 2 years and house had zero idea about any of his family issues and the neglect he experienced growing up. he worked with Cameron for about 7 years (they were even dating for roughly 4 of them) and its never once even alluded to that he had told her anything about what he had gone through.
he refused to talk about the dibala situation until he literally had zero choice.
in the episode titled 'one day, one room', house asks chase what he should tell the patient, to which chase responds "just keep her asleep".
while he can hold basic conversations and he can open up if he absolutely has to, he avoids it at all costs. while theres a plethora of reasons as to why this may be the case i think the two most likely are people never see him past his looks and the neglect he faced.
late in the show chase goes on a massive self-destructive sex streak as he learns that people are only nice to him because he's pretty. this suggests he's never really had to try in conversations with people as they are truly only interested in getting the chance to sleep with him and they couldn't really care less what he has to say. this also suggests he may have trust issues as he can never really tell when someone is being nice because they genuinely want to talk to him or wether they just want to sleep with him.
chase also detailed in s8 how he was greatly neglected by his alcoholic mother and absent father. this means he would've never really been taught any real social skills. while you may think school should've taught him those, its pretty likely he skipped a lot of school considering he had to take care of his mum and little sister. he learnt a lot of what he knows reading medical books when he was locked in his dads office.
chase has truly never had a real outlet for genuine conversation, so as a result he just tries to run away from it whenever he can.