Out of the blue, a longtime lawyer who works for the city’s Law Department yesterday declared she’ll challenge US Sen. Kirsten Gillibrand in the Democratic primary.

Gail Goode, 51, decided a couple weeks ago to launch her first campaign for public office because she was “offended” by reports that potential challengers were being muscled out of the race, said her spokesman, Jonathan Cohen.

“My candidacy may face long odds, but I’m used to taking on steep challenges,” said Goode, a former prosecutor in the Bronx DA’s Office and currently a trial supervisor at the Law Department.

“And given the anti-incumbent mood across the country and throughout the state right now, this is a great moment to be a challenger.”

Goode described herself as a social progressive who supports “equal marriage” and gun control.