Statistical procedures for variable selection have become integral elements in any analysis. Successful procedures are characterized by high predictive accuracy, yielding interpretable models while retaining computational efficiency. Penalized methods that perform coefficient shrinkage have been shown to be successful in many cases. Models with correlated predictors are particularly challenging to tackle. We propose a penalization procedure that performs variable selection while clustering groups of predictors automatically. The oracle properties of this procedure, including consistency in group identification, are also studied. The proposed method compares favorably with existing selection approaches in both prediction accuracy and model discovery, while retaining its computational efficiency. Supplementary materials are available online.