At present there is limited understanding of the host immune response to (low pathogenic) avian influenza virus infections in poultry. Here we develop a mathematical model for the innate immune response to avian influenza virus in chicken lung, describing the dynamics of viral load, interferon-α,-β and -γ, lung (i.e. pulmonary) cells and Natural Killer cells. We use recent results from experimentally infected chickens to validate some of the model predictions. The model includes an initial exponential increase of the viral load, which we show to be consistent with experimental data. Using this exponential growth model we show that the duration until a given viral load is reached in experiments with different inoculation doses is consistent with a model assuming a linear relationship between initial viral load and inoculation dose. Subsequent to the exponential-growth phase, the model results show a decline in viral load caused by both target-cell limitation as well as the innate immune response. The model results suggest that the temporal viral load pattern in the lungs displayed in experimental data cannot be explained by target-cell limitation alone. For biologically plausible parameter values the model is able to qualitatively match to data on viral load in chicken lungs up until approximately 4 days post infection. Comparison of model predictions with data on CD107-mediated degranulation of Natural Killer cells yields some discrepancy also for earlier days post infection.