The verb deign means to condescend to do something. When you deign to do something, you perceive the action to be beneath your dignity, but you do it anyway. In conventional usage, deign is always followed by to. So, for example, she doesn’t deign say hello would be incorrect, while she doesn’t deign to say hello would be correct.
These writers use deign well:
While Alexander was speaking, Reid and Pelosi wouldn’t even deign to look at him. [NY Times]
J.D. Salinger did not deign to write a separate reply. [Seattle PI]
Because deign is rare and a little tricky to use, writers come up with all sorts of interesting ways to misuse it. For example, these two writers incorrectly use deign as a synonym of dare:
I encourage readers to test my assertion in the News-Leader online forums; see how many ad hominem insults are generated when you deign to question collectivist dogma. [News-Leader]
I do not deign to educate you on matters you are no doubt more schooled in than I. [Democratic Underground]
This one incorrectly uses it as a synonym of deem:
They deign purchasers worthy of its use, so long as users abide by the legalese that blows past with every click of an “accept” button at the install screen. [Publicola]
And these writers incorrectly use it as a synonym of see fit to or decide:
The actual genesis of “new liberalism” would surprise many leftists, should they ever deign to study its true origins. [Canada Free Press]
. . . the images and results of the Games were shared in real time, often hours and hours before NBC would deign to offer them to the viewing public. [Kate O'Hare's Hot Cuppa Tea]