There is an urgent call to detect and prevent "biased data" at the earliest possible stage of the data pipelines used to build automated decision-making systems. In this paper, we are focusing on controlling the data bias in entity resolution (ER) tasks aiming to discover and unify records/descriptions from different data sources that refer to the same real-world entity. We formally define the ER problem with fairness constraints ensuring that all groups of entities have similar chances to be resolved. Then, we introduce FairER, a greedy algorithm for solving this problem for fairness criteria based on equal matching decisions. Our experiments show that FairER achieves similar or higher accuracy against two baseline methods over 7 datasets, while guaranteeing minimal bias.