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1. To search for and find someone or something. A noun or pronoun can be used between "chase" and "down." After an hour, the police were finally able to chase the criminal down. I went to five different hardware stores to chase down that part for the heater.
2. To drink two things in quick succession. A noun or pronoun can be used between "chase" and "down." Here, you'll need this to chase that shot down. It helps if you let them chase down the medicine with apple juice.
chase someone or something down
to track down and seize someone or something. Larry set out to chase the pickpocket down. The police chased down the suspect.