LOS ANGELES — When Alberto Fraire drives past a police car these days, he no longer worries about steep fines, or perhaps being hauled to jail and tangling with the immigration system. When California began issuing driver’s licenses to undocumented immigrants this year, he was one of the first in line.

“There’s a huge sense of relief now; it’s a psychological thing,” said Mr. Fraire, 37, who came to the United States with his parents from Mexico more than 25 years ago and recently leased a new black BMW to celebrate receiving his license in May. “I am not completely secure, but I don’t have to worry every time I get into my car.”

Mr. Fraire is part of an extraordinary milestone. In the first six months of this year, more than half of the new driver’s licenses issued by California went to undocumented immigrants like him.

Even now, months after the program went into effect, lines regularly begin at the Department of Motor Vehicles in Los Angeles by 6 a.m., a sign of the continuing changes in the state’s population. D.M.V. officials predict that they will issue nearly 1.5 million licenses to undocumented immigrants within three years. Of the 883,000 total licenses issued from January to the end of July, 443,000 were granted to undocumented immigrants, the officials said.