I don't need a chaser, tell that liquor come and get me
A chaser is something you drink right after taking a shot or swig of hard alcohol. So he is saying he is tough and doesn’t want to take the strength away from the liquor.
This is also a pun on the word “chaser”. He says that he doesn’t want a traditional chaser, and thus tells his liquor to “come and get [him]”, or chase him.
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