Of course the original cedar interior never had a finish applied since that would squelch the smell.
If you have cedar, make some fine shavings and put them in cheesecloth and tie it at the top. A couple or three bags thrown in the bottom of the chest should do it. When you cease to get a distinct whiff, repeat the process. If you don't have cedar, buy some cedar balls. They come in a bag. Distribute a few bags in the chest. Cedar oil is also available as somebody else pointed out.
You could also lightly sand the original boards, it'll help some but likely not enough.
Cedar balls on Amazon:
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- Renewing cedar smell in older chest + …