I also looked it up on wikipedia, and it looks like the endowment also owns the land underneath the Chrysler Building.

A substantial portion of the annual budget, which supports the full-tuition scholarships in addition to the school's costs, is generated through donations from alumni in both the public and the private sector. In addition, real estate has become a very important asset to the College and has drastically increased its endowment to over $600 million.[43] The land under the Chrysler Building is owned by the endowment,[44] and as of 2009, Cooper Union received $7 million per year from this parcel. Further, under a very unusual arrangement, New York City real-estate taxes assessed against the Chrysler lease, held by Tishman Speyer, are paid to Cooper Union, not the city. This arrangement would be voided if Cooper Union sold the real estate. In 2006, Tishman Speyer signed a deal with the school to pay rent that will escalate to $32.5 million in 2018, $41 million in 2028 and $55 million in 2038. Cooper Union investment committee member John Michaelson acknowledged to the Wall Street Journal that Tishman Speyer "would not have signed a generous agreement like that had it been approached in 2009."