Over time, an increasing proportion of imatinib-treated patients obtain a complete molecular response (CMR), defined as an undetectable molecular residual disease. In a previous study, STIM trial (PHRC 2006, stop Imatinib), 100 patients were included. The preliminary analysis among 69 patients having a median follow up of 21 months shows that the probability to maintain the CMR at 12 months is 45%. Our goal is actually to include up to 200 patients and then let the STIM opened during 3 years in a way to determine the predictive factors of the molecular relapse Discontinuation of treatment is proposed after checking selection criteria and signing informed consent. The assessment of BCR-ABL in peripheral blood by quantitative RT-PCR is performed every month during the first year then every two months second year then every three months during 3 years.