THE FEDERAL Election Commission has ruled that Gary Hart's restarted campaign is eligible for federal matching funds. That means the campaign will receive $100,000 immediately and probably another $900,000 or so on Jan. 11 when the FEC finishes examining his finance reports. This $1 million will be quite enough to enable Mr. Hart to run the minimalist campaign he has promised in New Hampshire, and if he is as successful there as he hopes to be, there can be little doubt that money enough will come flowing in over the transom, as it did for his 1984 campaign, to get him through the primary season.

The Hart campaign, which raised $2.2 million before the candidate left the race last May, seems eligible for these funds. The question now is what it will do with them -- and, specifically, whether it will use them to pay off the $1.1 million in debts remaining from the 1984 Hart campaign. The people who are owed that money are seeking an answer in a not entirely dispassionate way. Last April funds from a Hollywood fund-raiser were seized by Semper-Moser Associates of Venice, Calif.; in December a D.C. Superior Court granted Xerox a writ of attachment against the 1984 Hart campaign.

So far no creditor has gotten an order grabbing any of the 1988 proceeds. But many will keep trying. Small creditors like Semper-Moser may desperately need the money. Big creditors like Xerox may want to show they've made every effort to collect to avoid the charge that the debt amounts to an illegal corporate contribution. Mr. Hart says he wants to discuss serious ideas. But so long as he fails to pay his 1984 debts he may find himself trying to keep one step ahead of the sheriff.

Can Mr. Hart use 1988 funds to pay off 1984 debts? He has said the FEC says he can't, which is flat out wrong; he withdrew his request for an FEC opinion last October. His campaign manager says he might put 10 percent of his 1988 money in escrow to pay the debts, which will strike many creditors as too little too late. He should ask the FEC for another opinion, but that will take time too.

The best course is for Mr. Hart to start using the 1988 money to pay off 1984 debts as soon as he gets it. No other campaign is likely to complain that this is not a "qualified campaign expense" under current law. Mr. Hart can argue that it is, if only to help him campaign without harassment by creditors. The FEC may ultimately rule that it is not, but if it does there is only a civil penalty limited to the proportion -- probably about one-third -- that federal matching funds represent of his total 1988 campaign funds. And will the commission want to exact even that light penalty from a candidate who is doing nothing worse than paying off legitimate debts? Mr. Hart has said he wants to pay off his 1984 debts. The FEC is giving him the means to keep his promise. Will he?