Kepler's Goat Herd solves Kepler's equation using contour integration to solve the "geometric goat problem". The C++ code implements a variety of solution: 1.) Newton-Raphson: The quadratic Newton-Raphson root finder; 2.) Danby: The quartic root; 3.) Series: An elliptical series method; and 4.) Contour: A new method based on contour integration. Given an array of mean anomalies, an eccentricity and a desired precision, the code estimates the eccentric anomaly using each method. The accuracy of each approach is increased until the desired precision is reached, and timing is performed using the C++ chrono package.