The classical central limit theorem states that the average of an infinite sequence of independent and identically distributed random variables, when suitably rescaled, tends to a normal distribution. In fact, this classical result can be stated purely algebraically, using the combinatorics of pair partitions.  In the 1980s, Voiculescu proved an analog of the central limit theorem in free probability theory,  wherein the normal distribution is replaced by Wigner's semicircle distribution. Later, Speicher provided an algebraic proof of the free central limit theorem, based on the combinatorics of non-crossing pair partitions. Since then, various algebraic central limit theorems have been studied in noncommutative probability, for instance, in the context of symmetric groups. My talk will discuss a central limit theorem for the Thompson group F, and show that the central limit law of a naturally defined sequence in the group algebra of F is the normal distribution. Our combinatorial approach employs abstract reduction systems to arrive at this result.