From Longman Dictionary of Contemporary Englishchase somebody/something ↔ down phrasal verbto find something or someone that you have been looking for We had to chase down everyone we’d sold a bike to. → chase→ See Verb table
Examples from the Corpus
chase down• His glinting nails swish and clink as he chases me down a long hallway hung with pictures of CEOs.• Freddy Krueger is chasing you down an alley, his knives raised menacingly.• Why did he have to chase him down like an old lover?• I was literally soaked to the skin and could feel rivulets chasing each other down my bosom.• One even chased me down the sidewalk to return a scarf I left on the seat.• The hound, which was shining with phosphorus, chased Sir Charles down the Yew Alley.• You may want to chase it all down with a $ 3 carafe of hot sake.• Wolves - dogs, as they soon became - became more useful as they could chase and pull down wounded prey. 