Rice University (originally Rice Institute) began teaching in 1912 and didn't charge tuition until 1965, as they were also amending their charter to admit other than white students. My understanding is that Rice still provides a relatively large amount of student aid compared to most elite universities.
Anecdotally, a number of my high school friends went to Rice and all claimed to be paying very little or nothing in tuition (2008). My high school girlfriend received a full ride offer there (as she did from Caltech, which is what she chose). IIRC 38 students from my high school graduation class received offers from Rice.
Rice actually has a lower-% of students receiving need based aid.[1] I think a key reason why Rice enters a lot of conversations re: value stems from Houston's low cost of living.
