Why did House hire Chase after Chase's dad called?

I see several possibilities here. Let me elaborate:

Option 1

After his time in prison, House is seen scrounging for a budget; so that he can restart his daignostics division. He has little morality about acquiring the funds, as he even tries to trick a patient into helping him.

Note: House never truly lied to the patient, but House did subtly manipulate the situation in favor of him getting the budget. He also considered taking money from the patient when the patient was not considered capable of making that decision; but he only toyed with the idea, he didn't actually go through with it.

House could have done the same with hiring Chase. If Chase proves to be capable enough (but let's say that other capable applicants are available), it might be in House's benefit to have a good rapport with Chase's dad.

Option 2

Remember that Chase really hates his dad. House tends to stay close to unsolved puzzles, as it's his hobby.

Everyone he hires has been a contradiction in some way:

• Foreman is a black ex-criminal who decided to turn his life around. Not only that, he's morally on a really high horse. Foreman is also somewhat arrogant about how criminals choose to be criminals. Which is not what you'd expect from someone who has had to climb the ladder starting from rock bottom. You'd expect Foreman to know that poverty can force people to turn to crime to survive, but instead he has a "rich people attitude" about it.
• Cameron could have become a pretty girl (model, trophy wife, ...) and yet she chose to pick a hard working profession even though it was not necessary. She also chose to marry someone with a terminal illness. Given her emotional character, it's surprising for her to knowingly take on this emotional load. Emotional people should avoid highly emotional situations, and yet Cameron does not.
• Chase hates his father. He tries to be everything his father is not. He feels abandoned by his father. Yet, he still chooses to be a doctor, the exact thing that Chase's dad has built his life around (especially after leaving Chase behind).

So I think this pattern of hiring the doctors with unlikely or inexplicable characters has repeated with Chase.

If you follow the show, House seems to like Chase the most on a personal level. Chase gets chastised the least by House. Foreman is too principled, Cameron is too emotional, and both of them are likely to be targeted by House, either through direct discussion or by House subtly testing their character by manipulating them.
Compared to Foreman and Cameron, Chase's character is never really analyzed. He is a happy go lucky dude, who may or may not be right about a diagnosis; but he is rarely ever considered as having personality flaws.
He wasn't even scrutinized for having sex with Cameron, while Cameron got considerably more flak for doing the exact same thing (sleeping with a coworker).

However, this may be because it's very hard to provoke Chase. He is laid back and does not care as much as Foreman and Cameron do. Chase has always taken House's jokes in stride, and he doesn't seem personally affected by it.

He's also a surgeon, which means that he specializes in the one field that House has no authority over. Chase is often seen as House's "secret agent" during operations, if House wants Chase to do something that the head of surgery would strongly disapprove of.

Option 3

This one comes from the comments, but it's a good point and should be offered as a real answer.

House is a contrarian. He does the opposite of what he is told.

Chase's dad could have called House, not to make sure that Chase got the job, but to make sure that he didn't. For example, he could have wanted Chase to stay in Australia, so that there was a bigger chance of him reconnecting with his dad. Maybe it was part of a larger plan to have Chase find a job in the same hospital that his dad works in.

Chase's dad asking House to not hire him, not only triggers House's need to be a contrarian, but it also speaks volumes about the problems that exist between Chase and his dad, which can also support option 2.

Somebody once told me "everybody lies". So House get a call. And whatever the person on the other side said House knew they were lying.
He hire Chase because he is smart BUT the additional bonus point for "lying case" helped.
Cameron was hired because she is pretty. Which for House meant she had do work harder than anyone to be where she is.
When Doctor Dad call House, Gregory knew that Chase position is not granted but earned by him through work.