Defense Department strategists have a recurring nightmare that comes closer to reality with every passing day. The Joint Chiefs of Staff have described it tersely: The Persian Gulf is the most dangerous place on Earth, the trouble spot where World War III is most likely to originate.

Yet they cannot permit hostile forces to grab control of this strategic waterway, which is the free world's oil faucet. We have had access to the military strategists' thinking, as it appears in classified Pentagon planning papers. These experts are determined to keep President Reagan's commitment to defend America's "vital interests" in the Persian Gulf.

While they are worried about the contentious Ayatollah Ruhollah Khomeini, who has proclaimed his fierce hatred of America, they are more worried about what will happen after he finally succumbs.

They fear that he will leave Iran in chaos and that the disciplined, underground, communist Tudeh party will seize power in Tehran. But they don't think the Marxist usurpers will be able to establish their authority over the entire country.

This could force Iran to appeal to the Soviets. The Soviets have two dozen divisions waiting just north of the Iranian border, practicing invasions of Iran.

A Soviet takeover of Iran would give the Kremlin power to stop the flow of oil to the West. Pentagon planners view this possibility as "intolerable." The United States would be compelled to resist, but U.S. conventional forces could not possibly stop the Soviet juggernaut. This could be accomplished only with nuclear weapons.

How real is this nuclear nightmare? Would the Kremlin dare to risk World War III even for the prize of Persian Gulf oil? The secret planning papers point out that the Soviets have demonstrated in Afghanistan that they are willing to use military power when the stakes are high enough. In a secret analysis, the Joint Chiefs of Staff have warned: "The Soviet invasion of Afghanistan in late 1979 demonstrated a willingness to apply direct military force to achieve political objectives."

Meanwhile, about 250,000 Soviet troops are prepared to move into Iran behind an awesome battle line of tanks. One secret report states that "the Soviets have established command and control capability necessary to conduct large-scale military operations {in Iran}."

The Defense Department experts doubt that the Soviets would halt short of the Persian Gulf for anything less than a credible threat of nuclear war. Indeed, one "limited strategic option" would give the U.S. commander 19 nuclear bombs at his disposal, to be dropped on the Soviet invaders as they pour through passageways in the mountains of northern Iran.

The concept of a nuclear confrontation limited to Iran could turn into the ultimate nightmare. How likely is the nuclear fuse to be ignited by events in Iran? The worried strategists in Washington still count on sanity to prevail. They hold grimly to the belief that the cautious elements on both sides will control the levers and somehow muddle through.