The effect of line tension on the contact angle between a small sessile drop (radius a few tens or a hundred mu m) and a solid substrate is analyzed. When the line tension is great enough, it induces a wetting ("drying") transition, in which the contact angle jumps discontinuously to 0. The droplet is then completely detached from the surface, which remains in contact only with the vapor. Another result is that even if the drop would have wet (spread on) the substrate when the drop was macroscopically large, it will not do so when it is a small droplet if the line tension is positive.