YOU'RE CLIMBING THE Acropolis in Athens, and you suddenly develop crushing chest pains. Or you're commuting to your hotel in Venice and the bag containing your high blood pressure pills falls out of the gondola. Or you come up from your first attempt at skin diving in Merida, Mexico, and find you have sharp pains in your knees.

How do you find the best available medical help?

You consult "Traveling Healthy," (Penguin Books, $7.95), a remarkable new medical guide for American and British travelers. There you'll discover that the Athenian hospital of choice for a tourist with a heart attack will accept you only if a doctor calls first. You'll learn that Italian pharmacists will fill your American prescription (and the name your medicine goes by in Italy will probably be listed in the section on drugs). You'll be advised that joint pain is a symptom of the bends, and referred to Merida's "Centro do Salud," which has a decompression chamber.

A hefty 560 pages, this guide probably provides more medical information than the average traveler thinks he needs in his suitcase. But for anyone planning an extended trip abroad -- and certainly for anyone who takes medications or has chronic illness like diabetes or heart disease -- the book is worth its weight in Pepto-Bismol. Its thoroughness, intelligence, and -- at least for disease and drug information -- its accuracy, are both impressive and reassuring.

The book's appearance is timely, since the graying of the American population means that more and more of those going abroad each year are elderly. And more people venture out of the country despite diseases like cancer or heart failure that need frequent medical attention.

"Traveling Healthy" represents a year-long, on-the-spot survey of doctors, hospitals, ambulance services and other facilities in 23 countries by journalist Sheilah M. Hillman and her husband Robert S. Hillman, a doctor and professor of medicine at the University of Washington.

It reads like a Guide Michelin to international medicine. For each country, and for the major cities within it, the guide lists public and private hospitals and their services, sources of English-speaking doctors, emergency telephone numbers, and even how to get special services like cancer chemotherapy, kidney dialysis or a checkup for a heart pacemaker.

It describes the duration and method of training for doctors, and the general quality and bedside manner to be expected in each country. It offers advice about choosing between the public hospital (often a good university teaching hospital) and the private on (frequently more expensive and less complete). And it cautions travelers about special health hazards -- like altitude and air pollution in Mexico City, heat prostration from hot public baths in Japan, pregnancy due to the unavailability of contraceptives in Ireland and bad drivers practically everywhere.

The book makes fascinating browsing not only for inveterate travelers but for anyone interested in health car. Of the countries surveyed (all of Europe plus Israel, Mexico and Japan), the worst places to be sick appear to be the U.S.S.R. and parts of Mexico. "The danger of parachuting over Acapulco Bay takes on an added dimension when you consider Acapulco's lack of medical facilities," comment the authors at the conclusion of that city's section.

And in the Soviet Union, if a hotel doctor suggests a trip to the hospital for tests, their advice is, "Resist. If at all possible, go no farther . . . Once in a hospital, even for a minor illness, you may find it very difficult to be discharged."

A few details tesify to be thoughfulness of the research. The Paris section warns travelers to have a French-speaking person call the ambulance service, since dispatchers at every emergency number hung up immediately when asked (in French) whether the caller could speak to someone who spoke English.

The chapter on West Germany informs North American tourists that if admitted to a hospital they will be treated exclusively by the expensive Chefartz (chef doctor), unless they specifically request a less expensive, less senior, but usually equally qualified staff member.

Travelers to Japan who have any medical problems are urged to wear an obvious bracelet or necklace with that information, since Japanese ambulance attendants consider it impolite to search an unconscious person or examine his wallet. (A Medic Alert bracelet and membership, which is a good idea for anyone with an illness or drug allergy, is available for $15 from Medic Alert Foundation Intnernational, P.O. Box 1009, Turlock, Calif. 95380.)

A language section provides the pronunciation for "I am sick" and "I speak only English" in 14 languages. Other vocabulary -- like "help!" "bee sting," "ulcer," and "difficulty breathing" -- is listed in each language (even Japanese) but not written phonetically, on the assumption that it will be easier for a sick traveler to point to the needed expression than produce it out loud.

The final chapters are like an abbreviated medical text, covering everything from C.P.R. (the method for resuscitating someone whose heart and breathing have stopped) to travelers's diarrhea or "turista." The information is clear and current -- for instance, the "turista" section has the latest on antibiotic treatment and prevention, as well as warnings on dangerous drugs not to try, such as chloramphenicol and Entero-Vioform, which are both sold extensively abroad. A long section on drugs lists commonly prescribed American medicines by both generic and brand names, describes their side effects, and provides the corresponding drug names on other countries. The illness and drug sections should be particularly useful for anyone who plans to travel with an illness, even high blood pressure, that can't be ignored during vacations.

There are only two risks that I can imagine might ensue from dependence on this valuable book. The first is that it contains so much information that a traveler might be tempted to treat himself too long for a truly dangerous illness, relying on the guide's medical advice when a doctor -- even a non-English-speaking one -- could do better. The second is that, to be used right, it must be perused before the trip. If you pack "Traveling Healthy" but don't check your insurance coverage or get copies of your prescriptions, you've already ignored some of the book's most valuable advice.