We investigate the effects of atmospheric circulation on the chemistry of the hot Jupiter HD 209458b. We use a simplified dynamical model and a robust chemical network, as opposed to previous studies which have used a three dimensional circulation model coupled to a simple chemical kinetics scheme. The temperature structure and distribution of the main atmospheric constituents are calculated in the limit of an atmosphere that rotates as a solid body with an equatorial rotation rate of 1 km/s. Such motion mimics a uniform zonal wind which resembles the equatorial superrotation structure found by three dimensional circulation models. The uneven heating of this tidally locked planet causes, even in the presence of such a strong zonal wind, large temperature contrasts between the dayside and nightside, of up to 800 K. This would result in important longitudinal variations of some molecular abundances if the atmosphere were at chemical equilibrium. The zonal wind, however, acts as a powerful disequilibrium process. We identify the existence of a pressure level of transition between two regimes, which may be located between 100 and 0.1 mbar depending on the molecule. Below this transition layer, chemical equilibrium holds, while above it, the zonal wind tends to homogenize the chemical composition of the atmosphere, bringing molecular abundances in the limb and nightside regions close to chemical equilibrium values characteristic of the dayside, i.e. producing an horizontal quenching effect in the abundances. Reasoning based on timescales arguments indicates that horizontal and vertical mixing are likely to compete in HD 209458b's atmosphere, producing a complex distribution where molecular abundances are quenched horizontally to dayside values and vertically to chemical equilibrium values characteristic of deep layers.