In their darkest political hours, a shining opportunity has emerged for Yasser Arafat and Menachem Begin. It is waiting to be seized.

In the wake of his unconditional and acrimonious ouster from Syria, Arafat was being measured for a political shroud. Certainly, with moderate, radical and ultra-radical forces within the Palestine Liberation Organization at each other's throats, the fortunes of the self-styled leader of the Palestinian cause seemed to be at an all-time low.

Begin, too, was having his problems. His country was politically divided; he was grappling ineffectually with a monstrous inflation rate, and his foray into Lebanon was turning into a quagmire that was making Israel's body politic sick at heart.

Yet for these two seemingly implacable foes, the moment represents one of history's genuine opportunities, a chance to rearrange the map and to take a step toward fulfilling each other's openly cherished dreams. Their apparent misfortunes represent a test of their stature as genuine leaders of courage and foresight, instead of shortsighted and mean-minded, basically insular, foes.

In fact, because of the troubles of Arafat and Begin, the time has never been riper for a renewal of real negotiations over the fate of the Palestinians and West Bank and Gaza autonomy.

To understand this apparent contradiction, one has to look at what actually happened, especially to Arafat. On the surface, Arafat had the look and feel of a defeated man, a leader without a base, whose remaining followers were disheartened, disgruntled and all but captive within enemy territory. The PLO leader's ouster from Lebanon and Syria left Arafat in the position of being a wandering Palestinian, with no visible political clout and no army. The uprising in the ranks of the PLO, including the defiance of the radical Fatah group, tore the PLO asunder as a genuine and effective movement. What is left today of the PLO--Arafat's followers, adrift in Tripoli; the radicals under the total domination of Syria--is a fragmented force without much effectiveness.

Yet in the long run, this series of disasters may have had the salutary effect of freeing Arafat. It made him a prisoner no longer, either of the radicals within his own ranks or of his fickle ally, in Syria. Although he appears to have mended some politicial fences, Arafat still has the opportunity to become what he's striven to be for so long--an acceptable Arab leader, a true champion of the Palestinian cause and even a moderate.

There are signs that what has befallen him may not have been as damaging as was immediately apparent. A wandering leader Arafat may be, a man without a country, but in the eyes of the Arab world and the rest of the world, he remains the one leader of stature the Palestinians have. The Palestinians think so too, as witnessed by their strong reactions to events in Syria, when Pales tinians in the West Bank and Gaza denounced Syrian President Hafez Assad and the PLO radicals and upheld Arafat as their champion.

Arafat has an opportunity to truly legitimize himself and his cause. He can now do whatever he wants. He can, for one thing, ac cept Egyptian President Hosni Mubarak's earlier offer to establish a Palestinian government-in-exile in Cairo. It is an offer Arafat has repeatedly rejected, but can now take up with no fear, because it would give him a base.

He can go much further. He can join in support of the dormant Reagan plan, by joining in negotiations along the lines of a Jordanian solution to the Palestinian problem, a solution supported by the moderate Arab states, especially Jordan, Egypt and, to a degree, Saudi Arabia, as well as the Labor Party in Israel.

He can offer to join in renewed negotiations over Palestinian autonomy, even though it would mean, for now, a half-a-loaf solution in terms of his own cherished dreams.

He can take the decisive step of recognizing Israel's right to exist as a state. Recognition of Israel is Arafat's final chip, but it is a chip that will act as a rejuvenator of his status and fortunes. It is a chip that will throw the ball into Begin's court, and undercut his adamant opposition to the PLO. For Arafat, it would be a gesture quite on the order of Sadat's trip to Jerusalem.

Begin, too, in the midst of his troubles, has an opportunity, a chance to be remembered not as an obstructionist but as a peacemaker. Like Arafat, he is beleaguered, but there is no serious political threat to his tenure, since the Labor Party is in almost total disarray. Israel's long and bloody stay in Lebanon has turned into a genuine quagmire, as casualties mount daily.

As a body politic, Israel has never been more divided. Inflation is running unchecked, and Begin has only recently managed to quell a bitter doctors' strike. The nation is still feeling the effects of the Sabra-Shatila massacre.

But if Arafat were eventually to seize the opportunity, Begin could also help change history, by once again instilling the autonomy talks with renewed vigor and meaning and by including Arafat in the talks. Autonomy, although it represents a partial solution, is Begin's invention, after all, making it difficult to doubt the Israeli prime minister's sincerity on the issue.

Begin has a lot to gain--by seizing the opportunity, he can stifle Labor opposition once and for all, be assured of a huge electoral victory in 1984, cement his frayed ties with the United States and, along with Arafat, can isolate Syria, the radical elements of the PLO, Libya and the Soviet Union in the Mideast. More than that, an aging Begin can assure himself that his place in Zionist and world history will be that of a peacemaker.

Much depends on Arafat. Israel and Begin can and will survive their present troubles. If Arafat misses the moment, if he clings to his demands of a Palestinian state now, if he fails to shed his traditional animosity toward Israel, his stature will shrink until he disappears altogether. What faces Arafat now is a chance in his lifetime to see at least a Palestinian entity, and an opportunity to check further Israeli settlements in the West Bank.

They say the test of a true leader is his personal and political courage, and Arafat now has a chance to show both his mettle and his vision. If he fails to see and grab the opportunity, he will condemn his people, the Palestinians, to decades of strife and homelessness.

There is, especially today, a light at the end of the Palestinian tunnel. The question remains whether Arafat and Begin have the vision to see the light and pursue it.