High entropy alloys (HEAs) are single phase crystals that consist of random solid solutions of multiple elements in approximately equal proportions. This class of novel materials have exhibited superb mechanical properties, such as high strength which is associated with the motion of dislocations (line defects). We propose a stochastic continuum model based on the Peierls--Nabarroframework for dislocations in an HEA from an atomistic model that incorporates the atomic level randomness. This approach provides a fundamental explanation to the origin of the high strength of HEAs based on the stochastic effects on the intrinsic strength.