This paper proposes acoustic event detection (AED) with classifier chains, a new classifier based on the probabilistic chain rule. The proposed AED with classifier chains consists of a gated recurrent unit and performs iterative binary detection of each event one by one. In each iteration, the event's activity is estimated and used to condition the next output based on the probabilistic chain rule to form classifier chains. Therefore, the proposed method can handle the interdependence among events upon classification, while the conventional AED methods with multiple binary classifiers with a linear layer and sigmoid function have placed an assumption of conditional independence. In the experiments with a real-recording dataset, the proposed method demonstrates its superior AED performance to a relative 14.80% improvement compared to a convolutional recurrent neural network baseline system with the multiple binary classifiers.