Which of the following conditions leads to a thickening of bone and possible fracture risk?

The condition that leads to a thickening of bone and possible fracture risk is osteopetrosis. This disorder is characterized by excessive accumulation of bone mass due to an imbalance in the normal process of bone remodeling. In osteopetrosis, osteoclasts, the cells responsible for bone resorption, are dysfunctional, resulting in an increase in bone density and mass. While the bones may appear denser on imaging studies, they often become structurally weaker, leading to a high risk of fractures despite the increased thickness.

Other conditions mentioned, such as osteoporosis, are characterized by decreased bone density and increased fracture risk, making the bones more fragile. Rickets involves the softening of bones in children due to vitamin D deficiency, leading to deformities rather than thickening. Paget's disease does involve abnormal bone remodeling, but it typically results in chaotic bone formation which can lead to weak areas and deformities rather than just thickening. Therefore, osteopetrosis clearly stands out as the condition that leads to both increased thickness and associated fracture risk.