ROME, AUG. 5 -- The Italian Chamber of Deputies gave Prime Minister Giovanni Goria's government its vote of confidence today, giving official birth to Italy's 47th postwar government.

Goria, a Christian Democrat and, at 44, Italy's youngest prime minister, won parliament's grudging support for his five-party coalition government after three days of often acerbic debate that included such divergent subjects as Italy's Persian Gulf policy and the propriety of President Francesco Cossiga's nomination of the former treasury minister as premier.

Tonight's vote in the Chamber of Deputies was 371 to 237 in favor of the Goria government. The Senate had approved the government last weekend.

Thus for the first time since March 3, when Socialist Bettino Craxi resigned after almost four years as prime minister, Italy has a new Cabinet that is not a caretaker government.

Few analysts believe it will come anywhere near matching the longevity of the Craxi government, however, because none of the problems that led to the breakdown of Craxi's five-party coalition has been resolved.

Goria is a compromise prime minister, tapped by President Cossiga because his party's real choice for the job, party secretary Ciriaco De Mita, was vetoed for the job by Craxi.

The instability of Goria's reconstituted coalition was made clear during the confidence debate that preceded the vote. Not only were his proposed policies, on everything from nuclear energy to foreign policy, questioned by the coalition's other parties, but his status and suitability for the job were attacked by some members of his own Christian Democratic Party.

Some Christian Democrats were rankled that President Cossiga had picked a relative youngster as premier, in a party whose titans are in their sixties or seventies, over party leader De Mita, who had openly sought the job.

Some Christian Democrats have challenged the leadership qualifications of Goria, who likes to describe himself as "an accountant who is also a politician." Carlo Donat Catin, a former health minister, said, "For me, Goria has always been and always will be nothing but an accountant."

However, Goria's experience as an economist, a former budget undersecretary and one-time treasury minister will help him stay in office through the fall, if only to shepherd the country's 1988 budget through parliament. After that, the consensus is, he will face serious trouble.

No one gives him much chance of lasting longer than April, when his party holds its annual convention. Some analysts even fear that he might falter as early as this fall, when the country is due to hold five controversial referendums on nuclear energy and judicial reform.

The Christian Democrats, the dominant party in the coalition, are opposed to the referendums, while Craxi's Socialist Party, the second largest in the government, supports them. The issue was one that led to the collapse of the five-party coalition last fall. Another was the bitter dispute between Craxi and De Mita over who should preside over the government. After Craxi had led the coalition for almost four years, De Mita demanded that a Christian Democrat, preferably himself, be allowed to preside because the Christian Democrats are by far the largest party.

Craxi refused to accept the principle, and the ensuing deadlock finally led to the dissolution of parliament and new elections in June in which both Craxi's Socialists and De Mita's Christian Democrats gained in strength at the cost of the Communist Party, Italy's second largest. But after the vote, De Mita's and Craxi's choices were limited to re-formation of their coalition along with the minor Republican, Liberal and Social Democratic parties.