MIAMI (AP) _ The nation's oldest air passenger service, whose seaplanes carried celebrities, outlaws and at least one fleeing dictator in its 70 years, may be grounded by financial losses and competition from modern jets.

Unless a buyer is found, the final islan-hopping Chalk's International Airlines' flight will splash down Dec. 15 on Biscayne Bay off Miami.

''It's a very sad moment. This is an item of living history that may bite the dust,'' said Harold Rifas, an attorney for financially troubled Resorts International Inc., which has owned Chalk's since 1974.

''It was an exciting, thrilling way to move people,'' said Rifas. ''It's really a depressing thing for me to handle this.''

Rifas said losses have been ''very, very substantial'' at Chalk's, whose 17-seat seaplanes were featured on the opening credits of the former hit series ''Miami Vice.''

Resorts reported losses of $2.3 million for the first half of 1989 for its airline operations, including Chalk's and Paradise Island Airlines, which carries travelers to Resorts' Bahamian casino complex.

Chalk's dropped its Paradise Island route last month and now operates three daily flights between Miami and the Bahamian island of Bimini.

Resorts itself is struggling with mounting debt and falling values of junk bonds used by Merv Griffin to finance acquisition of the company from developer Donald Trump last year.

The possible demise of Chalk's would end a direct link with Miami's flamboyant past as a mecca for such pioneer aviators as Amelia Earhart, Eastern Airlines founder Eddie Rickenbaker, Pan American Airways founder Juan Trippe and Glenn Curtiss of Curtiss Aviation.

In 1919, barnstormer and stunt pilot Arthur ''Pappy'' Chalk took a Curtiss F flying boat to Miami and tied up along the bayfront, where he pitched an umbrella and began offering $5 sightseeing flights.

During the next decades, Chalk's Caribbean island flights carried everyone from sunburned tourists to shady Prohibition-era rumrunners. Passenger manifests also included names such as Ernest Hemingway and Errol Flynn.

In 1933, a hail of bullets followed a Chalk's plane whisking deposed Cuban dictator Geraldo Machado into exile.

In 1972, a Chalk's crewman and pilot were wounded by two gunmen who commandeered an aircraft to Cuba. The crew and passengers returned to Miami the next day.

Five years later, 88-year-old Chalk died after falling from a tree he was trimming.

The only accident involving a Chalk's aircraft and resulting in an injury occurred in 1985, when a Grumman Mallard crashed after takeoff from Cat Cay south of Bimini. One the 12 passengers was injured.

''When you talk about amphibious aircraft you are going back to the origins of international air travel,'' said Donna Corbett at the Smithsonian National Air and Space Museum in Washington. ''It's really a look back to the beginnings.''

The museum is exhibiting a former Chalk's Grumman Goose, the forerunner of the Mallards now operated by the airline.

Ms. Corbett said 63-year-old Northwest Airlines in Eagan, Minn., outside Minneapolis, is officially the nation's oldest passenger ''airline,'' a designation that requires posted schedules and a federal license.

But she said Chalk's, which received airline status in the 1940s after years without firm, posted schedules, may lay claim to being the oldest passenger ''service'' and the last surviving scheduled seaplane operation in the United States.

Catalina Flying Boats discontinued seaplane service last year from Long Beach, Calif., to Catalina Island.

Like other seaplane services, Chalk's has been unable to compete with faster and larger jets.

Several airlines, including Pan Am, Eastern and Midway Airlines, have service to the Bahamas. Paradise Island Airlines now uses 50-seat Dash 7 planes to its private airstrip.

Resorts reported it lost $48.5 million for the first six months of 1989 on revenue of $223.7 million.