Drove away (6)
'drove away' is the definition.
(shooing is a kind of driving away)
This is all the clue.
(Another definition for shooed that I've seen is " Drove away".)
(Other definitions for chased that I've seen before include "Pursued, ran after" , "Engraved; rushed" , "Decorated metal with engraved or embossed work" , "Hunted" , "Pursued at speed" .)