Fisher's exact test distribution is, as its name states, exact, and can therefore be used
regardless of the sample characteristics.
It converges asymptotically to Chi-square distribution for a large and well balanced sample.
For a set of small, sparse, or unbalanced data,
the exact and asymptotic p-values can be quite different and may lead to opposite conclusions
concerning the hypothesis of interest.
The exact distribution becomes difficult to calculate with large samples or well-balanced tables,
but fortunately these are precisely the conditions where the chi-square distribution is