I read this in The Reformation by Owen Chadwick (part of the Penguin church history series). It says:
Soon schools where built, and in 1544 the first university of the New World, that of Mexico...
Wikipedia mentions a couple of old Mexican institutions, but gives 1540, 1551, and 1587 as their starting dates. Only one of these appears to have been initially founded as a university, but they all have the wrong date.
So, did Chadwick get the date wrong? Is he talking about a university that isn't listed on wikipedia (e.g. because it has since closed)?
This is a tricky question. The University of Santo Domingo was founded by papal bull in 1538, then authorized by royal decree in 1558. As an institution it predates either university founded on the mainland, even if the royal authorization post dates both.
He could possibly be referring to the Colegio de Santa Cruz de Tlatelolco. The problem is that the Colegio was established prior to the date given and that it's purpose was to basically be a seminary for indigenous peoples. That purpose was never quite realized in the way the Franciscans imagined though, and the Colegio ended up slotting into a role that the calmecac had in pre-Hispanic Nahua society, essentially functioning as a school for children of the indigenous elite.
Please write the whole sentence. What you wrote seems to imply that the university did something in 1544, but was in existence before that date.