There are multiple ways to access The Chronicle of Higher Education online, listed under its Classic Catalog entry.
The journal’s website has some free full-text articles available, but for access to all full-text articles (including locked articles at the journal’s website) you may either:
Go through the links indicated in the library catalog, which directs you through the proxy,
Or you may register at the journal’s website. When registering, you must use your WUSTL email address for full-text access.