Slow mo walking chicken video, watch the head movement.

Observation of our chickens, when a chicken walks the head is kept motionless and then moves quickly to a new position, repeating over and over again as the chicken moves forward.

...One theory is based on the idea that movement in the environment is more easily detected if the eye is still (i.e. in hold phases) and that movement parallax (Gibson, 1950) generated when the eye is moving contributes a monocular depth perception (Welty, 1963). Thus head bobbing is considered to alternately optimize these two modes of visual exploration. This and the following theory emphasize monocular vision because many birds' eyes are laterally placed and thus they have only a monocular
view of much of their visual field.

Frost (1978) proposes that the thrust may provide retinal image motion in a preferred velocity range. The idea is that there are units in the visual system optimally responsive to stimuli in the velocity range provided by thrusts, and further, that the absence of backwards movement of the head keeps these units in an unadapted state.
The above theories are, of course, not mutually exclusive and the actual explanation may well involve a combination of them....

...There are two kinds of thrusts, those with and without saccades. It is difficult to sustain a theory involving visual input during thrusts with saccades. However, both Welty's and Frost's theories about the possible function of head bobbing may be correct for the thrusts without saccades.