Neutrosophic sets are an extension of intuitionistic fuzzy sets, providing a new approach to uncertainty with their three components: Truth, indeterminacy, and falsity. These parameters can be assigned independently which makes their sum equal to at most three. Neutrosophic sets have been extensively employed in the new extensions of multicriteria decision making methods (MCDM) in the literature. Law firms who are business entities formed by one or more lawyers are associations of lawyers who practice law. We propose a neutrosophic analytic hierarchy process (NAHP) for comparing the performances of these law firms in this paper. The performance of law offices is comparatively measured by the proposed NAHP. Linguistic assessments are used in this process rather than exact numerical evaluations. The illustrative problem hierarchy includes four criteria and four alternatives are given.