Rabbit that's divided for burger (3)

I believe the answer is:

bun

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'rabbit' is the definition.
(I know that rabbit can be written as bun)

I can't explain the rest of the clue.

(Other definitions for bun that I've seen before include "One from Chelsea" , "Small rounded bread or cake" , "Tied hair" , "Hair in tight coil" , "Something from Bath or Chelsea" .)

I've seen this clue in The Independent.

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