Dozens of affluent Washington homes from Chevy Chase to Capitol Hill have been hit by silver thieves in recent weeks -- apparently, police say, part of a spreading pattern of burglaries that originated in the suburbs last fall when the price of the precious metal skyrocketed.

Several gangs, some young and inexperienced members, have been breaking into homes in Georgetown, Cleveland Park and Chevy Chase west of Rock Creek Park as well as Capitol Hill and the Gold Coast along upper 16th Street NW, raking in an estimated $500,000 to $1 million in silverware, coins and other goodies, according to D.C. police.

Just last Saturday, burglary squad detectives raided a house in Far Southwest, seizing $30,000 in silver and other items they say were stored there from at least two burglaries in Upper Northwest.

No one was at the house at the time of the raid, and no arrests were made, police said. However, they said that they are seeking arrest warrants for several suspects whom they plan to charge with receiving stolen goods.

The spiraling price of both silver and gold in recent months has triggered a marked increase in precious metal thefts by burglars not only here but throughout the county, police say.

Encouraged by coin and precious metal dealers advertising their eagerness to buy up silver and gold, thieves have joined ordinary citizens in bringing antique silver, gold coins and other precious items to dealers for quick sale, police say.

Silver closed at $21.25 an ounce and gold at $548 an ounce on the New York Commodity Exchange yesterday. Silver sold for as little as $6 an ounce 14 months ago.

Police in Montgomery County in suburban Maryland and Arlington and Fairfax counties in Virginia began reporting increased silver thefts from affluent homes last December and January. Now the phenomenon has spread to the District of Columbia.

In Saturday's raid, D.C. police said they seized a small hoard of antique silver and coins, several rare paintings, plus television sets and stereo equipment.

The burglars appeared to be concentrating on silver items, but they also picked up such random objects as portable TV's and a $5,000 Persian rug that they apparently were using as a bath mat in their Southwest home, said burglary squad Sgt. Stanley Causey.

In another case, thieves carefully lifted a set of precious silverware from an Upper Northwest home, then also grabbed an ironing board and some potted plants but left a mink coat.

"It was like they wanted to set up housekeeping," said the lady of the burgled house, who asked not to be identified.

Casuey said the silver thieves, many of whom appear to be "young semi-professionals," customarily break into houses at night, especially between 7 p.m. and midnight, when family members are often away visiting friends, dining out, or attending theater shows.

He said they also break into houses where there are signs that the owners are out of town, such as an accumulation of newspapers on the front porch.

Assistant Police Chief Maurice T. Turner urged homeowners to avoid such telltale signs and also leave their homes well lighted at all times and put double locks on their doors.

Both Turner and Causey noted a recent government survey indicating that nearly half the home burglaries in the nation are committed without force because homeowners do not always lock their windows and doors.

The survey, prepared by the Census Bureau for the Justice Department, estimated there were 2.98 million no-force burglaries in 1975, an average of 8,200 homes a day.