A new survey measuring the satisfaction of people taking their vehicles into dealerships for service ranks five Fiat Chrysler brands as the worst in the auto industry. The company's Jeep nameplate received the worst ratings among all 20 brands in the J.D. Power Customer Service Index, despite the fact that it's led the industry in sales growth over the last two years.

The 2014 Jeep Cherokee. Chrysler Group LLC

"These results are consistent with what we've seen in recent years," said Mike Battaglia, senior director of auto retail at J.D. Power. "They've been underperforming in customer service at dealerships relative to the rest of the industry." Read MoreAutomakers to drivers: Get that car fixed! The J.D. Power study is based on the responses of 70,000 owners and lessees of 2010 to 2014 model-year vehicles. Fiat Chrysler did not immediately respond to a request for comment. Since coming out of bankruptcy in 2009 under the ownership of Fiat, sales for the Chrysler, Dodge, Jeep and Ram brands have rebounded. Thanks to a slew of new models and fresh marketing, Fiat Chrysler's U.S. market share has climbed from 8.9 percent at the end of 2009, to 12.7 percent at the end of last year.



So why are Fiat Chrysler customers surveyed by J.D. Power not as happy as owners of other brands? One issue is that FCA dealers often handle all five brands under one roof, which presents more challenges than tending to just one brand, Battaglia said. And as sales of Jeep and Ram have surged, so has the number of vehicles being handled for basic service. Read MoreVolkswagen makes a big push to be No. 1

Another area where FCA service centers trail those of other brands involves basic customer service, such as the attentiveness of service managers and how quickly customers can pick up their vehicle after servicing.