It is known that one of the important use of Chi-square test is the application of goodness of fit test to any given data. It is not difficult to find many article describing how to fit a normal distribution to given data and check whether it is good or not? This implies that the use of Chi-square is allowed even for the continuous data. if it is not agreed upon then how would you test whether any continuous data follows a normal distribution or not? For example, I wish to test whether height of healthy children follows a normal distribution or not? The answer I know is yes. Another example, whether hemoglobin of school children follow a normal distribution or not? The answer to this lies in fitting a normal distribution to binned data based on the values of mean and SD and check whether the chi-square comes out to be significant or not? A non-significant answer will confirm that the height or hemoglobin follows normal distribution. It can be checked by the histograms also. So, to say that the chi-square cannot be applied to continuous data appears to be not correct.