The bill would prohibit universities from designating a specific area as the only place where students can speak freely.
One of the people supporting the legislation said the so-called "free speech zones" often are tiny and out of the way.
"They have nothing to do with free speech and everything to do with quarantining speech and censoring speech," said Tyler Coward of the Foundation for Individual Rights in Education.
Coward said the bill would make sure students' free speech rights -- as laid out by the First Amendment -- are not violated.
The measure would still let school officials control the time, place and manner of the speech or expression as long as they are reasonable and content neutral.