Inclusion Criteria:

• Ambulatory, postmenopausal women with osteoporosis (no vaginal bleeding for at least 2 years prior to trial entry)
• Free of severe or chronically disabling conditions other than osteoporosis that will impair ability to complete the trial
• Bone mineral density (BMD) T-score of at least -2.5 at the femoral neck, total hip, or lumbar spine (L1-L4, with at least 2 evaluable vertebrae), with or without atraumatic fracture or,
• Bone mineral density (BMD) T-score of at least -1.5 at the femoral neck, or total hip, or lumbar spine (L1-L4, with at least 2 evaluable vertebrae), and either 1 or more atraumatic vertebral fracture(s) or an atraumatic nonvertebral fracture in the opinion of the investigator. Nonvertebral fracture sites allowed are wrist, hip, pelvis, ribs,humerus,clavicle, leg (femur, tibia, and fibula, excluding the ankle).
• Serum calcium, PTH, alkaline phosphatase must be within normal reference range

Exclusion Criteria:

• Have an increased risk of osteosarcoma (bone tumor); this includes Paget's disease of bone, a previous bone tumor, or radiation involving the skeleton
• Are allergic or cannot tolerate teriparatide or zoledronic acid or any of their ingredients or components
• Are allergic to tetracycline
• Have a history of exposure to tetracycline therapy in the 3 months prior to trial entry
• Have participated in a prior parathyroid hormone (PTH) clinical trial or received prior treatment with teriparatide, PTH, or other related medications
• Have a vitamin D level below 10 ng/ml
• Have a condition that could possibly put one at risk for an adverse event due to the bone biopsy procedure (e.g. bleeding disorder)
• Have undergone two previous iliac crest bone biopsies (one in each iliac crest)
• Have taken any intravenous (IV) osteoporosis medication
• Have taken other oral osteoporosis medications and have not been off of them for a specific period of time before trial entry
• Have a history of certain cancers in the 5 years prior to trial entry
• Have active liver disease
• Have significantly impaired kidney function
• Currently have active or suspected diseases that affect the bones, other than osteoporosis
• Have active or recent history of significant gastrointestinal (stomach or intestinal) disorders
• Have been treated with certain glucocorticoids for more than 30 days in the past 1 year prior to trial entry