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I've seen serged seams on a '30s petticoat, but not a silk chiffon dress - if you can post pics (including closeups of the serging and where the seams join) we can help determine dating and whether the serging was added later.
Serging goes back to Victorian times but it first appears (in my experience) in menswear, workwear especially and then in women's lingerie in the '20s. Occasionally you can find it in dresses of the '30s but not fancy things like silk chiffon. Personally, even now, I don't think it should be used on silk chiffon because it's a bulky finishing technique that can weigh the fabric down so I recommend French seaming instead.