Dr. Karin Galil, lead author of the study in Thursday's New England Journal of Medicine, and other experts said it is much too early to propose such a change.
"When there are 20 or 30 estimates, we'll have a better measure of how well it's truly working," said Galil, who was an epidemiologist for the Centers for Disease Control and Prevention when she studied the outbreak and now works for a company developing a new antibiotic.
Seven earlier studies found the vaccine protected at least 71 percent of the children who got shots from developing the disease and kept the disease minor in nearly all those infected by the virus.
But the latest study tracked by far the worst performance of a vaccine that has cut the number of U.S. chicken pox cases by 80 percent since it was introduced in 1995.
The outbreak was at a day care center near Concord, N.H. A boy who had been vaccinated three years earlier came down with the virus on Dec. 1, 2000. By Jan. 11, 2001, it had spread to 24 other children — including 17 who also had been vaccinated.
As CBS News Correspondent Elizabeth Kaledinreports, there was no evidence of problems with the vaccine itself, so this one unusual outbreak among supposedly protected children is puzzling doctors and raising questions.
"It may very well change the way we give this vaccine," says Dr. Jeffrey Boscamp who calls it a red flag.
"It's just unexpected. We really thought the chicken pox vaccine was something that would confer lifelong immunity," he says.
New Hampshire does not require chicken pox vaccinations. About two-thirds of the children had been vaccinated; six of the seven unvaccinated children in the boy's class got sick.
The vaccine did keep the illness minor, Galil said. One boy was diagnosed with a single blister and developed only two more after that.
In addition, there is evidence the vaccine protects against shingles, a painful skin and nerve infection that strikes decades after chicken pox.
According to Kaledin, vaccine-weary parents and children may cringe at that notion of having a second shot, but the alternative -- a nation of unprotected adults -- will be a much bigger problem.
"We don't want anybody getting into adulthood without immunity. It's a much more serious disease in adults," says Boscamp.
The ailment's lack of virulence makes it hard to tell how the vaccine is working, said Dr. Harry Keyserling, a pediatrics professor at Emory University School of Medicine and chairman of the Georgia Department of Human Resources' Vaccine Registry Advisory Committee.
"The problem with breakthrough chicken pox is it's generally so mild that no one would seek medical attention," he said. "So unless an organized study is done to look at breakthrough disease after five or 10 years of vaccinations, we won't have the data that we need to make those types of decisions."
Keyserling, who was not involved in the study, said the most important finding was that children vaccinated at least three years before being exposed were more likely to get chicken pox than those who had more recent inoculations.