Can the average case of an algorithm be $O(n \log n)$ if the best case running time of an algorithm is $\Theta(n \log n)$?

Question

Let us suppose the best case running time of an algorithm is $\Theta(n \log n)$. Can the average case run time of the algorithm be $O(n \log n)$? Since $O(n\log n)$ would imply the value going even below $n \log n$ hence would be lower than the best case bound of $\Theta(n \log n)$. Is this possible?