Driving to work over slick streets yesterday, Fairfax County Supervisor John P. Shacochis (D-Dranesville) saw only one car stuck in the ice and slush: It was a county police cruiser immobilized when a broken tire chain wrapped itself around the car's axle.

Later at yesterday regular meeting of the Board of Supervisors, Supervisor Joseph Alexander (D-Lee) introduced a measure to seek an alternative to the use of chains for winter driving.

Alexander said he had heard conplaints from several poline officers about the chains, which have been required equipment on county police cruisers since late 1975 to save the cost of snow tires.

A prime complaint by the police officers is that the chains must be attached when there is heavy snow but must be removed when streets are cleared or the chains will break. When a police cruiser goes into an unplowed subdivision, the chains must go on: when the car returns to the snow-free main roads, they must come off, several police officers told a reporter.

When the chains break, they either hit a cruiser's fender, denting it, or swing up and wrap around the axle, halting the vehicle.

Besides that, the police said, the heavy chains slow them down."

I know that," said Supervisor Alexander. "I used to drive an ambulance and I know they hold you down. I talked to officers driving 10 cruisers who had to go through the process" of attaching and removing the chains "twice in one day," he said.

Cruisers were equipped with-snow tires in the winter until 1974, when it became too expensive, according to Edmund L. Castillo, county public information director. While the snow tires were on the cars, the regular-tred tires were stored.

The following year, the county decided to save money by keeping the snow tires on the cruisers all year in an effort to save money, but that turned out to be a false economy because the tires wore out more quickly.

Now the county equips the cruisers with radial ply tires for year-round use plus chains costing $8 or $9 a set for use in snow four inches deep and deeper, according to Lt. John Liggett, acting commander of the Franconia police station. Liggett, who said he would rather have snow tires, said the chains are usually put on and taken off at local service stations at a small charge.

One person less than enthusiastic about the current system of equipping emergency vehicles with chains is Board of Supervisors Chairman John C. Herrity (R).

Herrity recalled for a reporter that when he suffered a heart attack in December, 1975, he was taken to Fairfax Hospital by an ambulance equipped with chains.

The ambulance was on the Capital Beltway approaching the Gallows Road exit near the hospital when a chain came off, Herrity said. "They stopped the ambulance and I started cussing." He said he called out, 'What the hell are you stopping for?"

The answer, he said, was "we've" got to take the chains off. It's the regulation."