The present paper investigates the influence of environmental noise on a fairly realistic three-species food chain model based on the Leslie-Gower scheme. The self- growth parameter for the prey species is assumed to be perturbed by white noise characterized by a Gaussian distribution with mean zero and unit spectral density. Using tools borrowed from the nonlinear dynamical system theory, we study the dynamical behavior of the model system. The behavior of the stochastic system (perturbed one) is studied and the fluctuations in the populations are measured both analytically (for the linearized system) and numerically by computer simulation. Varying one of the control parameters in its range, while keeping all the others constant, we monitor the changes in the dynamical behavior of the model system, thereby fixing the regimes in which the system exhibits chaotic dynamics. Our study suggests that the trophic level (top, middle or bottom) at which a population is positioned, the amplitude of environmental noise and the population's susceptibility to environmental noise play key roles in how noise affects the population dynamics.