It was extinguished in about 15 minutes, according to Fire Chief Jack Parow. The fire appears to have started in what will be the second and third floor areas of the building above the parking garage.
"It was determined that the electrician hooked up the wrong set of wires" on the second floor, Parow said. It was not immediately clear which wires were incorrectly set.
Two of the units suffered fire damage on two interior and exterior walls, according to the department.
The building is one of a cluster of apartment buildings, called Kensington at Chelmsford, that will be located on the former site of the Banqueteer, which was a popular restaurant at 225 Littleton Road.
In various incarnations, the restaurant had been operating since the 1920s. The restaurant has been torn down, and the site is now being developed into a 144-unit apartment complex by the Dolben Company and the Commons Development Group.
The complex has been criticized by some town officials, with complaints ranging from its appearance, which a selectman said is not as aesthetically pleasing as the town was told it would be, to the estimated 80 to 100 students it will add to a school system already described as overburdened.
There were no injuries reported in the fire last night. Lowell, Billerica, and Westford fire departments responded with mutual aid, and Chelmsford police blocked off a section of Littleton Road on both sides of the construction site while firefighters put out the fire and searched the building to make sure the fire was completely extinguished.