Inclusion Criteria:  Male or female, aged at least 18 years. Histologically confirmed diagnosis of primary non-small lung cancer (NSCLC) on predominantly non-squamous histology. MRI or CT scan of the brain must be done prior to surgery as it is considered standard of care. Patients must be classified post-operatively as Stage IB, II, or IIIA on the basis of pathologic criteria. Confirmation by the central laboratory that the tumor harbors one of the 2 common EGFR mutations known to be associated with EGFR-TKI sensitivity (Ex19del, L858R), either alone or in combination with other EGFR mutations including T790M. Complete surgical resection of the primary NSCLC is mandatory. All gross disease must have been removed at the end of surgery. All surgical margins of resection must be negative for the tumor. Complete recovery from surgery and standard post-operative therapy (if applicable) at the time of randomization. World Health Organization Performance Status of 0 to 1. Female patients should be using adequate contraceptive measures, should not be breastfeeding, and must have a negative pregnancy test prior to the first dose of the study drug; or female patients must have evidence of non-child-bearing potential.  Exclusion Criteria:  Pre-operative or post-operative or planned radiation therapy for the current lung cancer Pre-operative (neo-adjuvant) platinum-based or other chemotherapy Any prior anticancer therapy Prior treatment with neoadjuvant or adjuvant EGFR-TKI at any time Major surgery (including primary tumor surgery, excluding placement of vascular access) within 4 weeks of the first dose of study drug Patients currently receiving medications or herbal supplements known to be potent inducers of cytochrome P450 (CYP) 3A4 Treatment with an investigational drug within five half-lives of the compound or any of its related material. Patients who have had only segmentectomies or wedge resections History of other malignancies, except: adequately treated non-melanoma skin cancer, curatively treated in-situ cancer, or other solid tumors curatively treated with no evidence of disease for > 5 years following the end of treatment. Any unresolved toxicities from prior therapy greater than CTCAE Grade 1 at the time of starting study treatment with the exception of alopecia and Grade 2, prior platinum-therapy related neuropathy. Any evidence of severe or uncontrolled systemic diseases, including uncontrolled hypertension and active bleeding diatheses; or active infection including hepatitis B, hepatitis C, and human immunodeficiency virus (HIV). Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product, or previous significant bowel resection that would preclude adequate absorption of AZD9291. Any of the following cardiac criteria: Mean resting corrected QT interval (QTc) >470 msec, obtained from 3 ECGs, using the screening clinic ECG Machine-derived QTc value. Any clinically important abnormalities in rhythm, conduction, or morphology of resting ECG. Any factors that increase the risk of QTc prolongation or risk of arrhythmic events, or unexplained sudden death under 40 years of age in first-degree relatives or any concomitant medication known to prolong the QT interval. Past medical history of ILD, drug-induced ILD, radiation pneumonitis which required steroid treatment, or any evidence of clinically active ILD. Inadequate bone marrow reserve or organ function.