The reaction F + H-2 --> FH + H is studied quantum mechanically at ultralow temperatures. The low temperature limit of its rate coefficient is controlled by the attractive van der Waals interaction and quantum mechanical threshold effects. When the fine-structure splitting of the fluorine atom is neglected, the rate coefficient passes through a minimum near 10 K and then increases to a constant value of 1.25 x 10(-12) cm(3) s(-1) at temperatures below 0.2 K. When it is included the ultralow temperature limit is reduced to 2.5 x 10(-13) cm(3) s(-1). The long duration of the collision allows tunneling through the repulsive barrier even in the limit of zero temperature.