Assamese is a morphologically rich, agglutinative and relatively free word order Indic language. Although spoken by nearly 30 million people, very little computational linguistic work has been done for this language. In this paper, we present our work on part of speech (POS) tagging for Assamese using the well-known Hidden Markov Model. Since no well-defined suitable tagset was available, we develop a tagset of 172 tags in consultation with experts in linguistics. For successful tagging, we examine relevant linguistic issues in Assamese. For unknown words, we perform simple morphological analysis to determine probable tags. Using a manually tagged corpus of about 10000 words for training, we obtain a tagging accuracy of nearly 87% for test inputs.