maybe under some specific conversations this could make sense in english as in this hypothetical conversation: "what does katerina eat when she is really angry/sad/mad/happy/silly?" to which the reply is "she eats a chicken" which would be what she does under those circumstances. so, i think eating 'a chicken' is fine in the right context, but agree that on a regular bases, like every wednesday night, 'k. eats chicken' makes more sense in that context.
I have added "a chicken" to the accepted alternatives, since "the chicken" was already there. However, I would suggest it is much less likely to be used than the simple "Kateřina is eating chicken."
With regard to "the," "Kateřina is eating the chicken"could mean that, for example, out of three available dishes, she has chosen the chicken dish, rather than that she is eating an actual chicken (also possible but less likely).
If the Czech natives on the team feel that "a" is completely inappropriate here, I will delete that alternative.