We have used video imaging and interferometric techniques to investigate the dynamics of spreading of drops of ^{4}He on a solid surface for temperatures ranging from 5.2 K (near the critical point) to 2.2 K (near T_{λ}). After an initial transient, the drops become pancake-shaped with a radius that grows as R(t)≈t^{α}, with α=0.149±0.002. The drops eventually begin to shrink due to evaporation driven by gravitational and curvature effects, which limits their lifetime to about 1000 s. Although helium completely wets the substrate, and the spreading takes place over a pre-existing adsorbed film, a distinct contact line with a contact angle of order one degree is visible throughout this process.