The chaotic behavior of the secondary asteroid in a system of binary asteroids due to the asphericity and orbital eccentricity is investigated analytically and numerically. The binary asteroids are modeled with a sphere-ellipsoid model, in which the secondary asteroid is ellipsoid. The first-order resonance is studied for different values of asphericity and eccentricity of the secondary asteroid. The results of the Chirikov method are verified by Poincare section which show good agreement between analytical and numerical methods. It is also shown that asphericity and eccentricity affect the size of resonance regions such that beyond the threshold value, the resonance overlapping occurs and widespread chaos is visible.