SAN FRANCISCO—California secession dreamers can begin collecting signatures to place a nationhood proposal on the November 2018 ballot, after language for the measure was approved this week by the state’s attorney general.

The notion of a “Calexit”—a highly improbable idea that would require an amendment to the U.S. Constitution—gained popularity on social media following President Donald Trump’s unexpected victory in November, mostly as a humorous expression of opposition to the new president, whose policies are at odds with the liberal state.