A chart of a family's history with regard to a particular genetic trait is called a:

Pedigree

Explanation:

Pedigree refers to a chart constructed to represent an inheritance pattern of a genetic trait within a family through multiple generations. In a pedigree, each horizontal row represents a separate generation. The earliest generation is shown at the top and the most recent generation is present at the bottom. Pedigrees analysis determines the modes of single-locus inheritance. For instance, an autosomal trait is expressed equally in males and females of the family while males are most likely to be affected with an X-linked trait.