A correction in the New York Times about the possibility of a Clinton-Gillibrand Democratic ticket declares, "Aside from the debate over a two-woman ticket, Ms. Gillibrand and Mrs. Clinton are both from New York, and the Constitution prohibits the election of a president and a vice president who are from the same state."
This is inaccurate on two counts. Mrs. Clinton isn't "from New York." One of her two residences is in New York; the other is in Washington, D.C. She's "from" Illinois, and/or Arkansas, and could try to get around the "same state" issue by establishing a residence in one of those two states. (Dick Cheney "moved" from Texas back to Wyoming in 2000.)
Secondly, there is no Constitutional prohibition on the election of a president and vice president from the same state. Snopes has an excellent summary and debunking of the situation here. The bottom line is that the prohibition isn't on the candidates but on the electors from the single state from which both candidates hail; the electors would have to vote for another party's vice presidential candidate, which would only be a problem in a very close election and might argue against the wisdom of a single-state ticket, but does not flatly prohibit it.
Update: The Times does correct its correction: "A correction in this space...overstated the limitations the Constitution places on two candidates from the same state running on the same presidential ticket."
Update: An earlier version of this post, since corrected, erroneously referred to a "Schumer-Gillibrand ticket." In other words, the correction to the correction itself required a correction.