Fault detection and diagnosis (FDD) plays an essential role of maintaining large-scale heating ventilation air conditioning (HVAC) systems for industrial usage. The process of selecting important features is a crucial step for FDD methods of HVAC components, such as chillers. A suitable feature selection method selects the minimum number of features to save the number of installing sensors, and simultaneously maximizes the FDD accuracy. According to the surveyed related works, it is found that most existing works only focus on maximizing the classification accuracy, and miss two important points. First, the misclassification costs of false positive and false negative are different for chiller FDD. Second, the selected feature subsets must be sequential for real-world applications. In this study, a cost-sensitive and sequential feature selection algorithm for chiller FDD is proposed to select the most important features using a back-tracing sequential forward feature selection (BT-SFS) algorithm. The ASHRAE dataset collected by project number 1043-RP is utilized. Support vector machine (SVM), which is proved to be one of the most effective FDD classification method for chillers in existing works, is employed for accuracy measurement. This work fills in the gap between theoretical HVAC FDD methods and real-world HVAC FDD applications.