Although imatinib is an effective treatment for chronic myelogenous leukemia (CML), and nearly all patients treated with imatinib attain some form of remission, imatinib does not completely eliminate leukemia, and if the imatinib treatment is stopped, all patients eventually relapse [Cortes et al. Clin.Cancer Res. 2005]. In [Kim et al, PLoS Comput. Bio. 2008], the authors presented a mathematical model for the dynamics of CML under imatinib treatment that incorporates the anti-leukemia immune response. We use the mathematical model in [Kim et al, PLoS Comput. Bio. 2008] to study strategic treatment interruptions (STIs) as a potential therapeutic strategy for CML patients. We present the results of numerous treatment programs in which imatinib treatment is temporarily stopped to stimulate and leverage the anti-leukemia immune response to combat CML. The simulations presented in this paper imply that treatment programs that involve STIs may prevent leukemia from relapsing and may prevent remission for significantly longer than continuous imatinib treatment. Moreover, in many cases, STIs may completely eliminate leukemic cells from the body. Thus, STIs may be a feasible clinical approach to enhancing the effects of imatinib treatment for CML. We study the effects of both the timing and the duration of the treatment interruption on the results of the treatment. We also present a sensitivity analysis of the results to the parameters in the mathematical model.