This paper presents a method that identifies musical chords in polyphonic musical signals. As musical chords mainly represent the harmony of music and are related to other musical elements such as melody and rhythm, the performance of chord recognition should improve if this interrelationship is taken into consideration. Nevertheless, this interrelationship has not been utilized in the literature as far as the authors are aware. In this paper, bass lines are utilized as clues for improving chord recognition because they can be regarded as an element of the melody. A probabilistic framework is devised to uniformly integrate bass lines extracted by using bass pitch estimation into a hypothesis-search-based chord recognition. To prune the hypothesis space of the search, the hypothesis reliability is defined as the weighted sum of three reliabilities: the likelihood of Gaussian Mixture Models for the observed features, the joint probability of chord and bass pitch, and the chord transition N-gram probability. Experimental results show that our method recognized the chord sequences of 150 songs in twelve Beatles albums; the average frame-rate accuracy of the results was 73.4%.