The main difference between high entropy alloys and conventional alloys is the solid solution strengthening effect, which shifts from a single element to a multi-element matrix. Little is known about the effectiveness of this effect at high temperatures. Face-centered cubic, equiatomic, and single crystalline high entropy alloy CrMnFeCoNi was pre-alloyed by arc-melting and cast as a single crystal using the Bridgman process. Mechanical characterization by creep testing were performed at temperatures of 700, 980, 1100, and 1200 °C at different loads under vacuum and compared to single-crystalline pure nickel. The results allow a direct assessment of the influence of the chemical composition without any disturbance by grain boundary sliding or diffusion. The results indicate different behaviors of single crystalline pure nickel and CrMnFeCoNi. At 700 °C CrMnFeCoNi is more creep-resistant than Ni, but at 980 °C both alloys show a nearly similar creep strength. Above 980 °C the creep behavior is identical and the solid solution strengthening effect of the CrMnFeCoNi alloy disappears.