  We construct an algebraic variety by resolving singularities of a quintic
Calabi-Yau threefold. The middle cohomology of the threefold is shown to
contain a piece coming from a pair of elliptic surfaces. The resulting quotient
is a two-dimensional Galois representation. By using the Lefschetz fixed-point
theorem in \'etale cohomology and counting points on the variety over finite
fields, this Galois representation is shown to be modular.
