Let A denote a real linear transformation on Cn which is symmetric and positive-definite relative to the real inner product Re〈z,w〉, z,w∈Cn. Let FA(Cn) denote the Fock space consisting of holomorphic functions on Cn which are square integrable with respect to the Gaussian measure dμA(z)=detRAΠne-Re〈Az,z〉. For w∈Cn, let ewA(z)=eA(z,w)=e-12Re〈Aw,w〉KA(z,w), z∈Cn, where KA is the reproducing kernel for FA(Cn). The main aim of this paper is to show that there exist a,b>0 such that the set of functions {ema+inbA:m,n∈Zn} forms a frame in FA. © 2010 Elsevier Inc.