The first inkling that something had gone wrong in rural Hardeman County, Tenn., came last winter when the local kitchen sinks started turning brown.

Then came reports from puzzled residents of the southwestern Tennessee farming region that their well water had developed a peculiar insecticide-like odor. When a rash of unexplained cases of stomach cramps and dizzy spells hit the area, federal and state health investigators moved in.

Their discovery - some 350,000 leaky 55-gallon drums of legally buried chemical waste on a nearby ridgetop owned by the Chicago-based Velsicol Chemical Co.-is likely to add another chapter to what is rapidly becoming a recurring chemical-age nightmare.

Velsicol admits that between 1965 and 1972 it dumped chemical waste at the site from its Memphis pesticide plant. But a company spokesman insists there is no concrete proof the 17 chemical contaminants identified thus far in the local well water came from its dump. Moreover, Velsicol says its dumping was perfectly legal under state laws at the time.

That leaves federal and state officials with a virtual sea of toxic chemicals - including some known carcinogens-apparently flowing into the local water supply and no clear villain on whom to place the blame.

If the Hardeman County problem seems Herculean it is by no means unique. Across the nation, new stores of nearly forgotten, highly toxic chemical waste seem to be oozing into the headlines every week. Federal officials estimate there may be as many as 400 more suspicious hazardous waste sites around the country. And no one seems to know who will pay to clean them up.

Some recent examples:

Authorities in Michigan, nervously keeping tabs on toxic chemicals leaking from a company dump in Montague into Lake Michigan, recently checked and were horrified to discover it could cost $100 million to clean up similar hazardous waste sites around the state. "There's no way we're going to ask the taxpayers to ante up for that," said a state official.

In Massachusetts, health officials got an emergency $1.3 million from the state legislature to remove 17,000 barrels of toxic chemicals leaking from an abandoned lot in Lowell into the Merrimac River, the water source for several downstream communities. State officials are pledged to try to recover the cleanup money from financial backers of the bankrupt disposal firm and those who originally shipped the waste to the site. But a state official concedes glumly: "We're not holding our breath waiting to get paid."

In the widely publicized Love Canal situation in Niagara Falls, N.Y., officials have estimated that preliminary cleanup costs alone will run to $8 million. "And that," says an Environmental Protection Agency official "is just to make the area liveable. We're not even talking about relocation costs."

Nearly 200 families may eventually have to be permanently moved out of the area where thousands of drums of cancer-causing chemicals have leaked into backyards and basements.

Who will pay? "There's no provision for the federal government to come riding to the rescue," says Fred Lindsey, an EPA official in charge of the agency's implementation section:

"It's kind of confusing," admits another EPA official, "I guess the one who pays is whoever gets left holding the bag,"

That could include, says EPA's senior hazardous waste official Steffen Plehn, any of an estimated 425,000 firms which generate toxic chemical waste, or the 25,000 or so firms that transport it, or another 25,000 firms that store, treat or dispose of it.

Beyond that broad spectrum, Plehn admits, the focus of the blame becomes less clear. "If a company is still legally tied to the stuff then I guess it's theirs," says Plehn. "If they've been able to unload it then I guess the blame goes with it."

In the end, Plehn said, the answer may lie with efforts by EPA to set up a national trust to pay to clean hazardous waste sites. The trust would come from a per-ton tax on waste as it is dumped and would be held for emergencies such as the Love Canal disaster.

The problem with such a solution, however, is that it will tax waste generators who may be complying with law today for the environmental sins of others in the past. "It's not fair, and more important it probably industry official who asked not to be identified.

Thus far, only Michigan has sought to force chemical waste generators to pay for the cleanup of hazardous sites, even though they may not be directly involved in the problem.

Earlier this year Michigan Attorney General Frank Kelly went to court to recoup $1 million the state spent to clean up a site in Pontiac. The site was so dangerous, officials said, that a spell of hot weather could have caused some of the chemicals to explode and send a toxic chemical cloud floating over the city's wealthy suburbs.

The state's efforts to force the issue were sidetracked, however, when about 17 big waste generators, including such names as Ford and Dow-Corning agreed to come up with an out-of-court settlement.

Right now Michigan it closely watching another site owned by the Hooker Chemical and plastics Corp. in Montague. There, quantities of C-56 - a chemical building block for several carcinogenic pesticides - is leaking into White Lake, an arm of Lake Michigan.

Hooker's disposal site, as well as others in the state, may be legal, said Stewart Freeman, an assistant state attorney general. "But even assuming it is legal we can still say: all right you contain it or you pay for it," he said.

Hooker also operated the Love Canal site in Niagara Falls before deeding the site to a local school district under threat, according to the company, of condemnation proceedings against it.

Under a preliminary agreement, Hooker agreed to pay up to $280,000 to help clean up the Love Canal site. A company spokesman said Hooker also is spending several hundred thousand dollars on its Montague, Mich., disposal site where 11,000 tons of toixc chemicals are buried.

But the spokesman said Hooker will not admit legal liability in either case. "There's no way you could get us to say we're responsible for what happened at Love Canal," he said. Hooker or any company would "fight like hell" in court if the cleanup bills were turned over to them, he said.

That test could come in Tennessee. So far no one has formally blamed Velsicol for the polluted water in Hardeman County. But state officials note there does not appear to be another source for the unusual array of chemicals - including suspecte carcinogens such as chlorobenzine, tetrachloroethelene and toluene - that have turned up in the area's water. In addition, a still-unreleased federal study has also concluded that chemicals from Velsicol's disposal site have leaked into nearby wells.

Velsicol officials are preparing to do their own study of the situation. Some have even hinted darkly that perhaps local residents put the chemicals in the wells themselves in an effort to force blame on the company.

"This is a puzzle and all the parts aren't together yet," says one Velsicol official. "We do know that once that ridge was supposed to be an ideal dumping location. Now there's some question whether it was so ideal after all."