  Motivated by the recent work of Hofman and Maldacena we construct a classical
string solution on the beta-deformed AdS_5 \times \tilde{S}^5 background. This
string solution is identified with a magnon state of the integrable spin chain
description of the N=1 supersymmetric beta-deformed gauge theory. The string
solution carries two angular momenta, an infinite J_1 and a finite J_2 which
classically can take arbitrary values. It corresponds to the magnon of charge
J_2 propagating on an infinite spin chain. We derive an exact dispersion
relation for this magnon from string theory.
