ONE OF THE WORLD'S greatest hotel construction booms is under way in Egypt's teeming capital, and not a minute too soon.

Cairo's chronic and acute shortage of decent hotel rooms is right up there with the telephone mess and the traffic chaos as an irritant to life, a drag on the national economy and a sure fire topic of conversation.

As one Egyptian hotel man put it, "A hotel in Egypt is like a gold mine," and the gold rush is on. Almost every major international chain has a hotel under construction here, and a score of other projects by independent developers are also in the works.

Nearly every foreigner here has his favorite hotel harror story. There's the one about the Iranian tour group that arrived with confirmed reservations only to be turned away and sent to Alexandria, 140 miles north, to find rooms. Or the assistant manager who whits in his hotel's coffee shop each morning while the guests who slept on rollaway beds in his office are shooed out.

Or the airline crew that was turned away after a long flight because the rooms their airline rents permanently had been given to someone else. Or the California tourists urgently notified not to come because the government preempted their rooms for a visiting delegation - a frequent occurrence that escalates confusion into chaos.

Cairo, a metropolitan area of about 11 million residents and a major political religious and tourist center, has only about 1,600 hotel rooms that meet international standards.

IN THE WORDS of the "practical guide" published by the American University, "do not hope to get reservations at major hotels on short notice. They are generally booked full for months ahead, in or out of the tourist season."

The statistics bear this out. At the Cairo Sheraton, the occupancy rate for February was 99.8 percent and the hotel has stopped taking reservations through April. The lowest occupancy rate among the four major hotels was that of the Mena House Oberoi, at the edge of town near the great pyramids, where it was 95.4 percent. In the United States a hotel can break even at 60 percent occupancy and is doing nicely at 70 percent, hotel officials say.

Cairo's hotel shortage is more than just an inconvenience. It is a serious drag on an economy in which tourism is the principal earner of foreign currency and a deterrent to the foreign businessmen whom Egypt is trying to entice.

According to the minister of tourism, Moheb Stino, tourism brought in about $640 million last year, more than oil, more than the Suez Canal, more than cotton. But that is only a fraction of what it could be if Egypt had enough airline seats and hotel rooms to met the demand. Stino set a target of $1.2 billion in tourist revenue by 1980, and the hotels that could make that attainable are under construction.

A second Hilton of 900 rooms, more than twice the size of the existing one, is being built right on the Nile in central Cairo. Sheraton is adding a second tower of 370 rooms to its present building and is working on a second Sheraton near the airport.

Meridien, the Air France hotel chain, is also adding a second Cairo hotel near the airport. The Washington-based Marriott Corp. has construction crews working day and night in a rush to complete its first hotel in Egypt on the site of an old Nileside palace. Other chains that have hotels under construction are Hyatt, Intercontinental and Holiday Inn, most of these will be Egyptian owned, with the foreign hotel chains providing the management services.

These are only the biggest and most prominent projects in a hotel boom that should begin to ease the shortage of rom by the end of this year. Statistics provided by the Ministry of Tourism say that 1,800 rooms in 23 separate hotels of all sizes and classes will open this year.

THE CAIRO HOTEL shortage is a recent phenomenon. Tour guides at Thomas Cook's travel agency recall that up until early 1974, rooms were available for the asking even at the Hilton, and hotel managers paid commissions to cab drivers who delivered prospective guests.

Since then, however, several things have happened. The economic "open door policy" of President Anwar Sadat has brought a flood of Western businessmen on exploratory tours. European and American tourists have rediscovered Egypt. The civil war in Lebanon sent a lot of Arab business activity to Cairo. And the sudden flow of oil wealth into Saudi Arabia and the Gulf emirates created a whole new class of rich Arabs looking for fun in easygoing, Arabic-speaking Cairo, where liquor and gambling are legal.

Travel agents and hotel executives say they will have no trouble filling the new hotels when they are ready for occupancy. "You know what we'll get?" said one. "We'll get a minimum of 70 percent occupancy. That's good business anywhere else."