"I recently got asked by a professor who is also one of my recommenders to apply for a PhD in their department. This professor is also a co-chair of that said department."
That means he wants you in, and that he knows you. In general recommendation letters serve the exact purpose of having someone who is minimally verifiable and known to have some minimum competencies to vouch for you. This is often meant to impede a random person who never delivers anything or maybe hasn't even graduated/got a job to apply for a program and be accepted based on faux papers. Sometimes, people will check in with the letters authors to ask further questions, which you should be comfortable with.
A co-char in the department knowing you and vouching for you basically renders the process of recommendation letters useless. If he disapproved of you, no recommendation letter would change his mind, and I've never heard of a recommendation letter smearing someone-'s reputation (they at worst look like some default encrypted message saying the writer doesn't really know the student). Someone who would badmouth you should (and normally would) refuse writing a recommendation letter for you.
However, recommendation letters may still be required as a formality, hence why the co-chair would write one himself, as there must be at least one letter attached to your application. Also, keep in mind that this gentlemen may no longer be in the department by the time your papers are evaluated, who knows, right?
I'd bet that this professor knows the rules of engagement, so he knows if it's okay or not to write a letter himself. If there is a conflict of interest, that should be on himself, not on you, who should not be in disfavor because a member of the committee appreciates you (unless you are family or something related, in which condition he would not be allowed in the commission to judge your case or vote for your acceptance or dismissal).
Finally, I'm only aware of programs that required at least two recommendation letters. I had to deliver 3 to apply for a master's program. So your others letters could and should be written by some independent third parties.