Empathy describes the capacity to feel, understand, and emotionally engage with what other people are experiencing. People have recently started to turn to online health communities to seek empathetic support when they undergo difficult situations such as suffering from a life-threatening disease, while others are there to provide empathetic support to those who need it. It is, therefore, important to detect the direction of empathy expressed in natural language. Previous studies only focus on the presence of empathy at a high-level and do not distinguish the direction of empathy that is expressed in textual messages. In this paper, we take one step further in the identification of perceived empathy from text by introducing IEMPATHIZE, a dataset of messages annotated with the direction of empathy exchanged in an online cancer network. We analyze user messages to identify the direction of empathy at a fine-grained level: seeking or providing empathy. Our dataset IEMPATHIZE serves as a challenging benchmark for studying empathy at a fine-grained level.