Background The CHA ₂ DS ₂ ‐VASc (congestive heart failure, hypertension, age ≥75 years, diabetes, previous stroke or TIA [transient ischemic attack], vascular disease, age 65 to 74 years, sex category female; 2 indicates 2 points, otherwise 1 point) scoring system is recommended to guide decisions on oral anticoagulation therapy for stroke prevention in patients with nonsurgery atrial fibrillation. A score ≥1 in men and ≥2 in women, corresponding to an annual stroke risk exceeding 1%, warrants long‐term oral anticoagulation provided the bleeding risk is acceptable. However, in patients with new‐onset postoperative atrial fibrillation, the optimal risk stratification method is unknown. The aim of this study was therefore to evaluate the CHA ₂ DS ₂ ‐VASc scoring system for estimating the 1‐year ischemic stroke risk in patients with new‐onset postoperative atrial fibrillation after coronary artery bypass grafting. Methods and Results All patients with new‐onset postoperative atrial fibrillation and without oral anticoagulation after first‐time isolated coronary artery bypass grafting performed in Sweden during 2007 to 2017 were eligible for this registry‐based observational cohort study. The 1‐year ischemic stroke rate at each step of the CHA ₂ DS ₂ ‐VASc score was estimated using a Kaplan‐Meier estimator. Of the 6368 patients included (mean age, 69.9 years; 81% men), >97% were treated with antiplatelet drugs. There were 147 ischemic strokes during the first year of follow‐up. The ischemic stroke rate at 1 year was 0.3%, 0.7%, and 1.5% in patients with CHA ₂ DS ₂ ‐VASc scores of 1, 2, and 3, respectively, and ≥2.3% in patients with a score ≥4. A sensitivity analysis, with the inclusion of patients on anticoagulants, was performed and supported the primary results. Conclusions Patients with new‐onset atrial fibrillation after coronary artery bypass grafting and a CHA ₂ DS ₂ ‐VASc score <3 have such a low 1‐year risk for ischemic stroke that oral anticoagulation therapy should probably be avoided.