As the top federal prosecutor in New Jersey, Chris Christie struck an unusual deal with Bristol-Myers Squibb.

In exchange for not charging the drugmaking giant with securities fraud, Christie’s office would require it to fund a professorship at Seton Hall University’s law school — Christie’s alma mater.

The $5 million gift, one component of a larger agreement between the company and prosecutors, was hailed by the school, in South Orange, N.J., as a cornerstone of its new center on business ethics....