Managers are ever seeking for better ways of managing their constraints to improve their company’s value chain performance and competitiveness. Although previous literature explored constraint management, it was inconclusive as to how constraint management could affect the value chain performance in tea processing chains. The purpose of this study is to determine the relationship between constraint management and firm value chain performance of tea processing firms. This study undertook an empirical study using survey questionnaire design to collect data. The respondents were production managers who have experience in production activities. The study applied multiple correlation and regression models to test the hypothesis. The results indicate that constraints management had a significant positive impact on improvement in quality, time, flexibility, cost and resource utilization in tea firms. This study provides a broad analysis of how organizations can improve their value chain performance for sustainable development by managing various constraints in the internal value chain. To the best of the authors’ knowledge, this is the first empirical study of the relationship between constraints management and value chain performance using data from tea processing firms operating in Kenya.