(1) If you are being chased in a dream, what is chasing you probably symbolizes something you are afraid of, either in your external life or - more commonly - in your inner self, your unconscious. For example, a woman who dreams of being chased by men is probably afraid of sex. (Freud would add that her dreams present, in disguise, an unconscious, repressed desire for sex.)
(2) If you are doing the chasing, the ‘you’ in your dream is probably your conscious ego and the thing you are chasing is almost certainly some part of yourself that frightens you. Chasing it away means disowning it, banishing it from your conscious life. It might be much better to try to integrate it into your conscious life. At the very least, get to know it and understand it.... A Dictionary of Dream Symbols
To dream of seeing a brood of chickens, denotes worry from many cares, some of which of which will prove to your profit. Young or half grown chickens, signify fortunate enterprises, but to make them so you will have to exert your physical strength.
To see chickens going to roost, enemies are planning to work you evil.
To eat them, denotes that selfishness will detract from your otherwise good name. Business and love will remain in precarious states.... Ten Thousand Dream Interpretation
This flightless bird may be pointing to personal characteristics and needs that you may not necessarily want to look at. Consider the activities in the dream, as well as the mood, and then attempt to make a good interpretation. Chickens can represent cowardliness, gossip, excessive talking, and powerlessness. They are not known for their intelligence or beauty, and their presence in your dream could be an invitation to get more serious and better focused.
The more positive suggestion in this dream is in that chickens lay eggs. Eggs are symbolic of something new and fragile. They represent life and development in its earliest forms and as such, their possibilities are limitless.... The Bedside Dream Dictionary