We study a dynamic ordered logit model for panel data with fixed effects. We establish the validity of a set of moment conditions that are free of the fixed effects and that can be computed using four or more periods of data. We establish sufficient conditions for these moment conditions to identify the regression coefficients, the autoregressive parameters, and the threshold parameters. The parameters can be estimated using the generalized method of moments. We document the performance of this estimator using Monte Carlo simulations and an empirical illustration to self-reported health status using the British Household Panel Survey.