Within the Industry 4.0 vision, digital twins (DTs) have gained great attention as a promising approach to improve remote monitoring and control by means of virtual representations of physical objects. However, while DTs are becoming more and more sophisticated and even adopted for mission-critical applications, their resilience assessment has not received the required consideration yet. This article originally proposes chaos engineering to assess and improve the resilience of DTs by testing multiple aspects of industrial environments in a coordinated, automated, and replicable manner. First, the article discusses why and how chaos engineering is promising to improve the resilience of DTs. Then, it identifies and introduces a set of chaos engineering profiles specifically designed to take into account the many aspects an industrial environment is composed of. Finally, it shows the feasibility of assessing the resilience of a proof-of-concept DT through a testbed based on widely-adopted, open-source tools.