In recent years, the widespread adoption of distributed microservice architectures within the industry has significantly increased the demand for enhanced system availability and robustness. Due to the complex service invocation paths and dependencies at enterprise-level microservice systems, it is challenging to locate the anomalies promptly during service invocations, thus causing intractable issues for normal system operations and maintenance. In this paper, we propose a Causal Heterogeneous grAph baSed framEwork for root cause analysis, namely CHASE, for microservice systems with multimodal data, including traces, logs, and system monitoring metrics. Specifically, related information is encoded into representative embeddings and further modeled by a multimodal invocation graph. Following that, anomaly detection is performed on each instance node with attentive heterogeneous message passing from its adjacent metric and log nodes. Finally, CHASE learns from the constructed hypergraph with hyperedges representing the flow of causality and performs root cause localization. We evaluate the proposed framework on two public microservice datasets with distinct attributes and compare with the state-of-the-art methods. The results show that CHASE achieves the average performance gain up to 36.2%(A@1) and 29.4%(Percentage@1), respectively to its best counterpart.