To follow (another) with the intent of overtaking and capturing
To look for and pursue (game) in order to capture or kill it
The following of another in an attempt to overtake and capture
To make run away
I don't mean to chase you out.
When he was little, I couldn't chase him away.
We chase butterflies, and sometimes catch one.
I might meet some tall, dark, handsome man on the way, and you'd chase him off.
Their food was the meat they killed in the chase, or seeds and roots, grubs or reptiles.