Currently, convolutional neural networks (CNNs) define the state of the art for multipitch tracking in music signals. Echo State Networks (ESNs), a recently introduced recurrent neural network architecture, achieved similar results as CNNs for various tasks, such as phoneme or digit recognition. However, they have not yet received much attention in the community of Music Information Retrieval. The core of ESNs is a group of unordered, randomly connected neurons, i.e., the reservoir, by which the low-dimensional input space is non-linearly transformed into a high-dimensional feature space. Because only the weights of the connections between the reservoir and the output are trained using linear regression, ESNs are easier to train than deep neural networks. This paper presents a first exploration of ESNs for the challenging task of multipitch tracking in music signals. The best results presented in this paper were achieved with a bidirectional two-layer ESN with 20 000 neurons in each layer. Although the final F-score of 0.7198 still falls below the state of the art (0.7370), the proposed ESN-based approach serves as a baseline for further investigations of ESNs in audio signal processing in the future.