In this paper, the authors study an initial-boundary value problem of Othmer-Stevens chemotaxis system with reaction term in the master equation
{∂u/∂t=D∨(u ∨ln u/Φ(x, t, w))+ f(x, t, u),
∂w/∂t=g(x, t, u, w),
u∨ln u/Φ(x, t, w) ?n→=0.
They prove that there exists a unique solution if the boundary ∂Ω ∈C2+β, the functions Φ(x, t, w), f(x, t, u) and g(x, t, u, w) are sufficiently smooth.