Two old foes lead three-way battle for Massachusetts governor's chair,

Can the Duke dethrone the King?

A hard-fought campaign is shaping up for the governor's chair in Massachusetts, where the state's conservative Democratic Gov. -Edward J. King is facing a stiff primary battle with former Gov. Michael S. Dukakis, whom King deposed four years ago.

The primary battle, which also includes Lt. Gov. Thomas P. O'Neill III, gained considerable momentum over the past weekend with key political moves by all three contenders, including the Mr. Dukakis's declaration of candidacy.

Although it is early in the race, voter opinion samplings over the past several months appear to favor Dukakis (whom the state's public and press have nicknamed ''the Duke'') by a wide margin over both his rivals for the Democratic nomination.

Property tax relief and public safety appear to be the dominant issues.

Dukakis is calling for 20 percent of the state's revenue growth to be shared with the cities and towns to help them make ends meet and provide additional police protection. He does not favor boosting taxes and says any move in that direction should be ''only as a last resort.''

Lt. Governor O'Neill also is calling for expanded local aid, but using a different approach. He would reduce state spending while adding a 1 percent hike in the state's current 5 percent limited sales tax.

Governor King, on the other hand, until recently held out little hope for additional aid to municipal governments in the coming fiscal year. Instead, his priority was lowering the state's personal income tax. Last week, however, he changed his tune somewhat, indicating that he hoped relief in both directions could be provided.

Nowhere, however, do the candidates differ more greatly than on law enforcement.

King, whose 1978 gubernatorial campaign rested substantially on a strong law-and-order plank, including the advocacy of tough mandatory sentences and a restoration of capital punishment, has renewed his call for the latter.

Dukakis, on the other hand, is not about to compromise his longstanding opposition to the death penalty. Decrying the rise in the crime rate in the years since he left office, the former governor says he favors the presence of more and better-trained police to improve public safety.

In launching his comeback offensive Jan. 10, Dukakis pledged an administration dedicated to the principles of ''integrity, competence, compassion, and effectiveness.''

He emphasized that implementing the recommendations of a special commission that probed state political corruption would be given his early attention as governor.

The former governor, elected in 1974, is a liberal who during four years in office was free of even the hint of scandal. He was upset by conservative Democrat King in the 1978 Democratic primary.

Lt. Governor O'Neill, the son of US House Speaker Thomas P. O'Neill Jr. (D) of Massachusetts, is projecting himself as a compromise candidate, embracing the best of the approachs of his ballot foes.

All three are expected to seek endorsement at the party's preprimary convention in May. Although the outcome there is not binding, it could give the winner a push toward the nomination in the September primary.

The winner then will face the victor of what looks to be a Republican scramble. Five GOP gubernatorial candidates have launched their campaigns within the past two months. Most, if not all, of them will compete for endorsement at the March 6 Republican preprimary convention.

Some Dukakis boosters view his greatest challenge as avoiding being dragged into a low-level, name-calling battle with the man who defeated him four years ago.

Some analysts say the election could be a referendum on Reaganomics. Governor King has been generally supportive of Republican President Reagan's policies; Dukakis has been critical of them. So, too, has O'Neill, who in 1980 headed the New England campaign of US Sen. Edward M. Kennedy (D) of Massachusetts for the presidential nomination.