But she faces a tough slate of rivals, one of whom is likely to force her into a runoff, according to political professionals.
Ten candidates originally entered the race, but the field narrowed to four last week after election officials weeded out the hopefuls who failed to submit nominating petitions with the required signatures of 500 registered voters.
In addition to Yaroslavsky, the other candidates are Mike Feuer, the former head of a legal clinic; Roberta Weintraub, a former Los Angeles school board president, and Jeff Brain, a Sherman Oaks businessman.
Yaroslavsky is the wife of Zev Yaroslavsky, the councilman who represented the district for 19 years before he resigned in December to take a seat on the County Board of Supervisors. The district stretches from Sherman Oaks to Brentwood, Fairfax and other Westside communities.
Among those eliminated from the race last week was Lea Purwin D'Agostino, a deputy district attorney who had the backing of the union that represents the rank and file of the Los Angeles Police Department.
It is still not clear who will benefit from D'Agostino's departure but her absence is expected to spark a scramble among the remaining candidates to pick up the union's endorsement and take up the role of "law-and-order" candidate.
Feuer's supporters say he would be interested in the endorsement. They note he has already advocated a "tough on crime" stand by drafting a plan to establish police substations in the district.
Although union leaders have vowed to oppose Barbara Yaroslavsky because they blame Zev Yaroslavsky for holding up police union contract negotiations last year, she still holds out hope that they will consider endorsing her.
"We hope they will take another look at her candidacy," said Laurie Saffian, Yaroslavsky's campaign manager.
Police union officials planned to meet Wednesday to consider whether to endorse another candidate.
In the April 11 primaries, a candidate who can garner more than half of the vote automatically wins the seat and does not have to face a runoff on June 6.
Yaroslavsky has a well-recognized name and a $279,000 campaign war chest--more than twice the funds of any other candidate. Still, political professionals say they would be surprised to see her draw more than half the vote away from the three other candidates.
"I regard her as a front-runner, but not as a shoo-in," said Arnold Steinberg, a Valley-based political strategist.
Yaroslavsky's rivals also seem to recognize her as the front-runner. In recent candidates' forums, the other hopefuls have mostly aimed their criticism at Yaroslavsky instead of at each other.
For the most part, she has defended herself but not returned fire with her own criticism.
Steinberg and other consultants who have been watching the race said Yaroslavsky seems to have a strong base of support among liberal Jewish Westside voters. But with a well-defined campaign, they said, she may be able to expand her base to include more conservative voters in the Valley.
Because all three candidates are well-funded, Steve Afriat, a Hollywood-based political consultant, said he expects none of the candidates to win a majority of the vote in April.
He predicts a June 6 runoff between Yaroslavsky and Weintraub, who he believes will draw most of her support from the Valley.
Others say Yaroslavsky's toughest challenger will be Feuer, who has raised $119,000 and also draws most of his support from liberal Westside voters.