Right under one's nose

It would be understood, but right under his nose is the usual phrase.

Thanks a lot, BJ.

I made a mistake.

Here's the correct one:

The thief stole Jim's wallet right under his nose.

Is it possible to say "in front of" instead of under?

I misread what you wrote, and interpreted it to mean what you intended it to mean.
The thief stole Jim's wallet right in front of his nose would be readily understood, although under is the more usual version.
The thief stole Jim's wallet in front of under his nose would sound very odd indeed, and although the person you were talking to would proba

Thank you for your reply, BJ.