Well you learn something new every day! I found this on a quilting site:

http://lequilts.com/?page_id=38

Can I keep my quilts in a cedar chest?
Cedar, along with other woods, secretes oils that can damage fabric. If you must keep your quilts in a wooden container, it should be sealed with a protective coating of polyurethane varnish, then lined with unbleached, washed muslin or acid-free paper. Metal containers should also be lined with this muslin or paper.

Here is a good article about preservation of treasured textiles:
http://www.mohistory.org/img/unCommo..._treasures.pdf

#6 on the list mentions cedar chests.

Just a thought - if you seal the inside of the cedar chest with polyurethane that will also eliminate the insect repellent properties.

I have stored in Cedar chest for years without damage. However, my sister had wood worms eat through her cedar chest and leave a small hole and then nested in her linens. My DH says this is possible if they used some of the sap wood (the wood on the outside of the tree) instead of the heart wood (the wood on the inside of the tree). Cedar woods contain oil but not acid. I think the difference is the fact that in old cedar chests, the oil has dried out and thus no stain on the linens.
There is a chemical in the wood but it is not acid. Acid is in cardboard, paper and tissue paper and comes from the paper making process.

With all due respect to your DH, acids and oils are present in all wood and wood products, cedar included. Acid may be increased by the paper making process, I don't know, but it's definitely present within the tree itself before any processing. It's one reason why tree mulches, even cedar mulch, increase the acidity of your soil.

To the OP, some here have had good experiences storing in cedar or other wooden chests, some have not. Even unsealed wooden shelves and corrugated cardboard boxes can discolor and deteriorate the fibers of textiles. Examples have been given on several other threads over the years, some are truly heartbreaking. Only you can decided what your risk tolerance is.

I was told that the wood would eventually harm the fabric that I stored in mine. I lined the inside with self sticking shelf lining and have never had a problem. The lining is slightly tacky so it adhears to the wood. I taped the seams with masking tape so it stays together. It works for me!

Fabric needs to breath. Storing them in the chest would cut off all air. If you do store them in the chest be sure to take them out at least every six months to air them. Do put them in an old pillow case before storing.

I never knew this either. I would have thought it would have been a great idea because the cedar would keep moths away. Hmmm. Glad you asked this question!

I went to an estate sale a while back and scraps from quilts and also quilts were stored in a cedar chest. They had stains because of not being stored or wrapped in tissue paper. I purchased a lot of the scraps. The odor from the cedar was really hard to get out of the scraps. A friend of mine purchased the last quilt. She soaked and washed and repeated several times with ammonia and arm and hammer detergent and borax and vinegar (as I did the same with the scraps). She then hung the quilt outside for some fresh air. Took forever but now the quilt just smells fresh and clean and looks great on her bed. She had to do a couple repairs (not too much)just tucking some threads in here and there. She found that the quilt had been handed down generations and was hand quilted in 1911. She has a pic of it. No matter how old anything is she gives it a purpose. I'll have to see if I can get a photo of it.

As far as I know the only things NOT recommended to store in a cedar chest are metals or papers of any kind. They were made for linens so I can't see how putting quilts in them is bad. I've had some baby quilts stored in mine for over 20 yrs. and they are still in perfect condition.