Would it be so bad to add the wood chips to the keg and carb up... taste test for a few weeks or so, then remove the chips?

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I'm also thinking that you could hang the chips from the lid of the keg so that once you pull a few pints out its not sitting in the beer anymore?
I ask because i have a kickass christmas ale i made that has been aging now a month (after fermentation stopped) and I want to add a bit oak flavor to it but not enough to take away from the work its done on its own.