The purpose of this study is to determine the feasibility of administering the combination of nilotinib and LDE225 to patients with chronic or accelerated phase of chronic myeloid leukemia and to establish the maximum tolerated dose (MTD) and/or recommended Phase II dose level (RP2D) of LDE225 in combination with nilotinib.

Inclusion Criteria:

1. Philadelphia chromosome positive (Ph+) CML in chronic phase (CP) or accelerated phase (AP)with resistance to at least one prior BCR-ABL targeting TKI
2. Documented chronic phase CML
3. Adequate end organ function
4. Female patients of childbearing potential must have a negative serum pregnancy test and must be using highly effective methods of contraception. Male patients with female partners of child-bearing potential must use condoms.

Exclusion Criteria:

1. Impaired cardiac function
2. Severe and/or uncontrolled concurrent disease that in the opinion of the investigator could cause unacceptable safety risks or compromise compliance with the protocol
3. History of acute pancreatitis within 1 year of study entry or past medical history of chronic pancreatitis
4. Patients actively receiving therapy with strong CYP3A4 inhibitors and/or inducers, and the treatment cannot be either discontinued or switched to a different medication prior to entering the study
5. Patients who are currently receiving treatment with any medications that have the potential to prolong the QT interval and the treatment cannot be either safely discontinued or switched to a different medication prior to starting study drug.
6. Previously documented BCR-ABL Y253H, E255K/V, T315I or F359C/V mutation

Other protocol-defined inclusion/exclusion criteria may apply.