OVERCOMING ideological hang-ups about allowing foreigners to own private property in China, the government has decided to sell off bits of the country at US$100 a piece. Dubbed ''Own a piece of homeland of China'', the campaign is aimed at raking in nearly $1 billion from overseas Chinese. Other foreigners are not eligible to buy the minuscule plots. The programme appears to be an imitation of a US scheme which, for $49.95, offered foreigners a square inch of terrain in each of the 50 states of America. Believing, erroneously, that buying the US deeds would entitle them to a US visa, mainland Chinese paid up to $1,700 for their tiny piece of America. China's project involves setting up 36 ''homeland gardens''. That means one garden in each province, autonomous region or self-governing municipality. Taiwan, Hongkong and Macau will each have their own garden, although the logistics of planning these gardens are unclear since China does not control these regions. Each garden will have an area of 9.6 million square inches, symbolising the 9.6 million square kilometre land area of China, according to Mr Liu Yi, chairman of the China National Tourism Administration. For $100, overseas Chinese may buy certificates entitling them to one square inch in each of the homeland gardens, and the right to visit the gardens free of admission charge. Mr Liu admitted that the organisers had not given any thought to planning the Taiwan garden. He promised that the Hongkong and Macau gardens would be managed according to local regulations. Ownership of private property has been a politically sensitive issue in China, particularly when foreigners are involved. But, said Mr Liu, ''this goes beyond ideology''. Mr Zou Yuchuan, director of the state land bureau, said the certificates would entitle the owners to land-use rights, which currently are for a maximum of 70 years in China. But those rights could be extended, and the land handed down to descendants for hundreds of years, Mr Zou said. The names of owners would be engraved on a wall in the Beijing garden ''in order of heavenly stems and earthly branches'', said Mr Liu. In other gardens, all records of ownership would be kept on computer files. Proceeds from sales will go to help the handicapped, develop science and technology and develop China's travel industry. The project is sponsored by, among others, the State Sports Commission and the China Welfare Fund for the Handicapped. The 33 mainland gardens are expected to be finished by the end of 1995.