Compound words with unmarked word boundaries are problematic for many tasks in NLP and computational linguistics, including information extraction, machine translation, and syllabification. This paper introduces a simple, proof-of-concept language modeling approach to automatic compound segmentation, as applied to Finnish. This approach utilizes an off-the-shelf morphological analyzer to split training words into their constituent morphemes. A language model is subsequently trained on ngrams composed of morphemes, morpheme boundaries, and word boundaries. Linguistic constraints are then used to weed out phonotactically ill-formed segmentations, thereby allowing the language model to select the best grammatical segmentation. This approach achieves an accuracy of ~97%.