A classical field theory of gravity and electromagnetism is developed. The starting point of the theory is the Maxwell equations which are directly tied to the Riemann-Christoffel curvature tensor. This is done through the derivatives of the Maxwell tensor which are equated to a vector field  contracted with the curvature tensor, i.e., . The electromagnetic portion of the theory is shown to be equivalent to the classical Maxwell equations with the addition of a hidden variable. Because the proposed equations describing electromagnetism and gravity differ from the classical Maxwell-Einstein equations, their ability to describe classical physics is shown for several situations by direct calculation. The inclusion of antimatter and its behavior in a gravitational field, and the possibility of particle-like solutions exhibiting quantized charge, mass and angular momentum are discussed.