Intense linearly polarized light induces a dipole force that aligns an anisotropic molecule to the direction of the field polarization. Rotating the polarization causes the molecule to rotate. Using femtosecond laser technology, we accelerate the rate of rotation from 0 to 6 THz in 50 ps, spinning chlorine molecules from near rest up to angular momentum states J approximately 420. At the highest spinning rate, the molecular bond is broken and the molecule dissociates.