In this study the aim is to recruit 66 patients who have treated and well controlled blood pressure but may still have LVH. They will be screened for LVH by doing an ultrasound scan of the heart and then that will be confirmed with a Magnetic Resonance Imaging (MRI) scan, which is a special scan of the heart using an MRI machine to measure the extent of thickening of the heart muscle before they start on treatment of allopurinol or placebo.