A Giffen good is one that does not about the 'law of demand' in that the good has an UPWARD sloping demand curve. This means that as the price rises, MORE of the good is demanded, rather than less (and vice versa)
Studies on the proof of existence of true Giffen goods are sparse due to the difficulty in observation of consumer choices and controlling for all variables. However, it is not inconceivable that in areas of extreme poverty, the existence of Giffen goods is possible. Staple foods such as rice, which people need to eat in suitable quantities in order to simply survive, could be classified as a Giffen good for some people. When the price of rice increases (relative to other goods), the proportion of the income that needs to be spent on food for survival might increase and if there is no substitute for rice then the demand for rice might possibly increase.