Every week up to 70 more people infected with the condition arrive at the hospital, situated off the city's northern ring road, seeking whatever help is available.
The staff do what they can. For illnesses associated with Aids, such as tuberculosis, they can do quite a lot to help to control the pain and improve a patient's quality of life.
But for Aids they can do nothing. In Gaborone - as elsewhere around the country - there is simply not the money for the expensive anti-viral drugs used in the West to slow the effects of the disease. Drugs to treat one person for a month cost the same as a senior civil servant's salary.
"It is extremely depressing. Our wards are full of young people aged 20 to 35 dying, and that is something we are not used to," said Dr Howard Moffat, a consultant physician and the hospital's acting superintendent. "I was here when we diagnosed out first Aids case in 1986. Since then the growth in the number of cases we have witnessed has been phenomenal. And we only see a small number of those people who are suffering."
Botswana and neighbouring Zimbabwe share the unenviable honour of being the Aids capitals of the world. In both of these southern African countries 25 per cent of adults aged between 15 and 49 are infected with either HIV or Aids. In Botswana, a country with a population of just 1.5 million, this means that between 200,000 to 220,000 are infected with the virus.
Botswana's problem, as elsewhere, is one of attitudes being slow to change. An aggressive health education campaign in English and Setswana has meant that most people are aware of the dangers of Aids. Yet in a country where 95 per cent of HIV infection is spread through sexual activity, many people are still reluctant to change their behaviour. "One problem is that many young people only see the disease as something that might affect them in 10 or 15 years," said Dr Moffat. "While the infection rates of HIV are high, the number of people who have died has only increased since 1992. Now, the number of people who have died from Aids has reached 15,000 but attitudes are slow to change."
Trying to convince people to use condoms is another problem. In the past where people have used any contraception, it has usually been oral.
In Botswana condoms are as easily available as Coca-Cola. Clare Short, the Secretary of State for Overseas Development, says condoms need to be as widely available as Coca-Cola if Aids is to be tackled in the developing world. But whereas the "Real Thing" costs the equivalent of 20p for 330mls, a packet of contraceptives costs five times as much.
"Condoms are available free of charge from health centres but people have to queue up for them. There is a problem with this because it is hard to persuade people to go and collect them," said another Gaborone- based health worker employed by the United Nations.
"A lot of men simply don't want to go to health centres and get these things. If the Government is going to persuade people to use them it is going to have to try and ensure condoms are available elsewhere.
"One difficulty is that until recently Aids has not been a visible problem. It has been easy for people to think it will not affect them."
That situation is rapidly changing. While experts believe the percentage of people infected is unlikely to rise further, the actual number of people developing full-blown Aids will increase.
And Aids is not just affecting adults. In Princess Marina Hospital, built in 1966 to celebrate the country's independence from Britain, 25 per cent of the infants receiving treatment are babies born infected with HIV.
And the children's wards at the hospital, like those set aside for adults, are full.