Workplace Prospective new employer wants to contact my current employer

Just to give an update, I was offered the job and accepted!

I definitely hadn't experienced this before, but will be a little more savvy in the future. It's strange, because I had a lot of people (including acquaintances in HR and recruiting) telling me not to let them speak with my current employer, but then based on the conversations here I see that it's common practice.

In any case, University A was satisfied with simply viewing my recent performance review and and speaking with two other references.

Super excited about this opportunity! Thanks again for everyone's input!