Ultracold molecules promise new scientific explorations, including novel molecular interactions, quantum chemical reactions, exotic phase transitions, and strongly correlated states of matter. We recently produced a near-quantum degenerate gas of polar molecules in their absolute ground state. With all degrees of freedom under precise control, we have for the first time observed chemical reactions at ultralow temperatures. We control the reaction rates with pure long-range, quantum mechanical effects, achieving state-by-state analysis of reaction dynamics. The long-range and anisotropic nature of the dipolar interaction has also been observed.