The rural, poverty-ridden Chatham area of Southside Virginia has the highest infant mortality rate in the state. It is first in the rate of teen-agers' abortions. It also has one of the state's highest rates of venereal disease.

Two years ago, to cope with its pressing health problems, Chatham built with federal funding a $700,000 medical clinic. Yet the clinic has not treated a single patient.

The clinic's doors remain locked and its rooms empty because the facility has no doctors. Chatham's establishment, loath to accept further federal aid, tried vainly for a year to attract private physicians.

Chatham has finally accepted a $242,000 federal grant from the Rural Health Initiative Program to equip the clinic and recruit doctors. Although the doctors are not yet hired, the town is likely to get some who owe service to the government because they obtained U.S. aid to get through medical school.

Clinic administrator Rosemary Axelrod who, besides trying to recruit doctors, has had very little administering to do, says the failure to attract doctors "bothers me a lot . . . It's very sad. The need is here. People have severe health problems and we can't get the doctors."

Former town manager Paul Harold, who was instrumental in getting the clinic built, ran into opposition from the local establishment when we wanted to get additional federal help to find and hire physicians.

"Doctors don't want to come to rural areas," Harold said. Yet, he added, the establishment, including local doctors, "pressed to continue looking in the private sector, and that's impossible."

Local officials had a list of 300 physicians who were seeking a practice in a rural area, but most of them wanted amenities like nearby mountains or the seashore. "We didn't have either," said Harold.

About 10 doctors did come for interviews, he added, but none decided to stay.

Among those who opposed more involvement was Dr. Gerard Thompson Sr., a member of the local health facilities planning agency.

"I don't think the federal government has any business in medicine," said Thompson. "It will lead to socialized medicine. I think supply will catch up with demand it we're a little patient.

Finally, however, Chatham was faced with accepting more federal dollars or continuing to maintain a costly clinic that served no one. The town chose the former.

"This is one of the most conservative areas in the country," said Hunter A. Grumbles, administrator of Danville Memorial Hospital in nearby Danville, near the North Carolina border. "But when you get down to the bare facts, and you say it's costing $20,000 annually to maintain a building that's not being used, the decision comes easily."

Even with the $242,000 federal grant in hand, it could still be another year before Chatham's clinic is open, according to Axelrod. New doctors make their plans at least a year in advance. The earliest arrival is now expected to be July 1981.

Meanwhile, Chatham's clinic will have exactly the kind of red tape many of the town's residents oppose so deeply. The federal government will set a ceiling on the doctors' salaries -- not more than $40,000 a year. The physicians will be required to follow federal health rules and standards of care, and will not be able to charge their patients directly.

During the three-year gap between the clinic's construction and the expected date when it will open, the Chatham area's 20,000 residents are relying on five local doctors, two of whom are about to retire.

The patient-doctor load, said Harold, is about four times higher than what it should be.