When dealing with the chi-square goodness-of-fit test, we are trying to find out if the sample in question comes from the population with the claimed distribution.
Now, the idea behind this concept is that if the observed value is very close to the expected/claimed value, it means the square of the deviations will now be small. The weighted square deviations will now be calculated and if their sum is small, it means the observed values will be close to the expected values and there would thus be no reason to reject the claim that it came from the distribution. Thus, it's only when the sum is large, that there would be a reason for questioning the distribution.
Thus, goodness of fit tests are always right tailed tests.
