Kriging is intensively used to interpolate costly deterministic computer experiments. Since many recent advances in simulation rely on probabilistic methods (Monte Carlo, etc...), it becomes necessary to take their randomness into account. Here we present an adaptation of the "Nugget Effect", originally developed in geostatistics to model observational noise, to the frame of computer experiments with tunable probabilistic noise. We propose a statistical model for such simulators, give a derivation of the associated Kriging equations (KEPH), and discuss the estimation of the covariance parameters. We finally consider perspectives such as the use of KEPH for noisy-simulator-based uncertainty propagation or optimization strategies.