 This is an open label single arm feasibility trial. A combination of two oral agents pravastatin and lonafarnib and one intravenous IV agent zoledronic acid will be administered at doses and schedule currently applied in pediatrics. These agents all target farnesylation pathways at different points. Our goal is to inhibit farnesylation of abnormal lamin, the disease-causing protein in Hutchinson-Gilford Progeria Syndrome and progeroid laminopathies henceforth progeria. The drugs will include the intravenous bisphosphonate zoledronic acid, oral HMG co-reductase inhibitor pravastatin and the oral farnesyltransferase inhibitor FTI lonafarnib SCH 66336. Patients with genetically confirmed progeria will be eligible for this protocol. Treatment will be initiated for 4 weeks duration and may be extended depending on tolerability. This study will assess the feasibility of this treatment regimen in the first 4 weeks. If tolerated for 4 weeks, patients can be treated with this regimen for up to 6 months. 