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Hierarchical Agglomerative Clustering (HAC) algorithms are extensively utilized in modern data science, and seek to partition the dataset into clusters while generating a hierarchical relationship between the data samples. HAC algorithms are employed in many applications, such as biology, natural language processing, and recommender systems. Thus, it is imperative to ensure that these algorithms are fair -- even if the dataset contains biases against certain protected groups, the cluster outputs generated should not discriminate against samples from any of these groups. However, recent work in clustering fairness has mostly focused on center-based clustering algorithms, such as k-median and k-means clustering. In this paper, we propose fair algorithms for performing HAC that enforce fairness constraints 1) irrespective of the distance linkage criteria used, 2) generalize to any natural measures of clustering fairness for HAC, 3) work for multiple protected groups, and 4) have competitive running times to vanilla HAC. Through extensive experiments on multiple real-world UCI datasets, we show that our proposed algorithm finds fairer clusterings compared to vanilla HAC as well as other state-of-the-art fair clustering approaches.