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Please bring one chair from the next room.
Literal
Next [of-の] room [from-から] chair [object-を] one take-come [please-ください].
一つ ('one') as a counter for a general object. 取ってくる ('to take and come back') is the compound 取る + くる — 'go fetch.' Subtly different from 持ってくる ('to bring'): 取ってくる emphasizes the going-to-get-it motion, while 持ってくる highlights the carrying-back-with-you part.