Background: Tyrosine kinase inhibitors (TKIs) have improved the survival of patients with chronic myeloid leukaemia. Many patients have deep molecular responses, a prerequisite for TKI therapy discontinuation. We aimed to define precise conditions for stopping treatment. Methods: In this prospective, non-randomised trial, we enrolled patients with chronic myeloid leukaemia at 61 European centres in 11 countries. Eligible patients had chronic-phase chronic myeloid leukaemia, had received any TKI for at least 3 years (without treatment failure according to European LeukemiaNet [ELN] recommendations), and had a confirmed deep molecular response for at least 1 year. The primary endpoint was molecular relapse-free survival, defined by loss of major molecular response (MMR; >0·1% BCR-ABL1 on the International Scale) and assessed in all patients with at least one molecular result. Secondary endpoints were a prognostic analysis of factors affecting maintenance of MMR at 6 months in learning and validation samples and the cost impact of stopping TKI therapy. We considered loss of haematological response, progress to accelerated-phase chronic myeloid leukaemia, or blast crisis as serious adverse events. This study presents the results of the prespecified interim analysis, which was done after the 6-month molecular relapse-free survival status was known for 200 patients. The study is ongoing and is registered with ClinicalTrials.gov, number NCT01596114. Findings: Between May 30, 2012, and Dec 3, 2014, we assessed 868 patients with chronic myeloid leukaemia for eligibility, of whom 758 were enrolled. Median follow-up of the 755 patients evaluable for molecular response was 27 months (IQR 21–34). Molecular relapse-free survival for these patients was 61% (95% CI 57–64) at 6 months and 50% (46–54) at 24 months. Of these 755 patients, 371 (49%) lost MMR after TKI discontinuation, four (1%) died while in MMR for reasons unrelated to chronic myeloid leukaemia (myocardial infarction, lung cancer, renal cancer, and heart failure), and 13 (2%) restarted TKI therapy while in MMR. A further six (1%) patients died in chronic-phase chronic myeloid leukaemia after loss of MMR and re-initiation of TKI therapy for reasons unrelated to chronic myeloid leukaemia, and two (<1%) patients lost MMR despite restarting TKI therapy. In the prognostic analysis in 405 patients who received imatinib as first-line treatment (learning sample), longer treatment duration (odds ratio [OR] per year 1·14 [95% CI 1·05–1·23]; p=0·0010) and longer deep molecular response durations (1·13 [1·04–1·23]; p=0·0032) were associated with increasing probability of MMR maintenance at 6 months. The OR for deep molecular response duration was replicated in the validation sample consisting of 171 patients treated with any TKI as first-line treatment, although the association was not significant (1·13 [0·98–1·29]; p=0·08). TKI discontinuation was associated with substantial cost savings (an estimated €22 million). No serious adverse events were reported. Interpretation: Patients with chronic myeloid leukaemia who have achieved deep molecular responses have good molecular relapse-free survival. Such patients should be considered for TKI discontinuation, particularly those who have been in deep molecular response for a long time. Stopping treatment could spare patients from treatment-induced side-effects and reduce health expenditure. Funding: ELN Foundation and France National Cancer Institute.