My mom used to read me a book that she thinks was by golden books and
was either called the Chatter Duck or had a character chatter duck in
it. How and where do I find it with so little information?

I have found two titles that may interest you: "Chatterduck" and
"Chatterduck and the Plump Pig," both written by Helen and Alf Evers.

Used copies of "Chatterduck" may be purchased here:

Alibris
http://www.alibris.com/search/detail.cfm?BID=8070916291

Alibris
http://www.alibris.com/search/detail.cfm?BID=8133863050

AntiQbook
http://www.antiqbook.com/books/bookinfo.phtml?nr=65033794

ABE Books
http://dogbert.abebooks.com/abe/BookDetails?bi=59982668

ABE Books
http://dogbert.abebooks.com/abe/BookDetails?bi=194948690

ABE Books
http://dogbert.abebooks.com/abe/BookDetails?bi=80202989

ABE Books
http://dogbert.abebooks.com/abe/BookDetails?bi=109547398

ABE Books
http://dogbert.abebooks.com/abe/BookDetails?bi=199020588

ABE Books
http://dogbert.abebooks.com/abe/BookDetails?bi=14129238

ABE Books
http://dogbert.abebooks.com/abe/BookDetails?bi=190115230

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Used copies of "Chatterduck and the Plump Pig" may be purchased here:

Alibris
http://www.alibris.com/search/detail.cfm?BID=8133628324

ABE Books
http://dogbert.abebooks.com/abe/BookDetails?bi=74642082

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There is also one copy of "Chatterduck" offered on eBay. This is worth
looking at, since the seller has included a photo of the book's cover,
which may jog your memory:

http://half.ebay.com/account/include/frame/ebayFrame.jsp?target=ebay_query&search_string=%28%22chatterduck%22%29

To locate these books, I used the excellent used book search available
at addall.com:

Condensed search link for AddAll
http://tinyurl.com/9fq8

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I hope this helps you to obtain a copy of the book you remember. If I
have misidentified the book, or if a link does not function, please
give me a chance to provide clarification before you rate my answer.

Best wishes,
pinkfreud

Good Job pinkfreud!