Hi Dave. Welcome to the Village. We're glad you found us. I think you'll have a good time here. Lots of friendly folks to chat with and pick their brains.
As far as chipping, the first thing I'd look at is your blades. Most of the blades you find at a hardware store are not very good. They're intended mostly for construction type work, not for hobbiests. The three big brands are Flying Dutchman (a lot of folks buy from Mike's Workshop), Olson, and Pegas. Quality blades make all the difference in the world. You'll also want finer teeth. The bigger the teeth, the more tear-out you'll get. My favorite blade is the Flying Dutchman Scroll-Reverse #3 for plywood 1/8"-1/4". A #3 or #5 will work nicely on 1/4"-3/4".
The next thing to look at is the plywood you're using. Birch plywood, especially from the home improvement stores, aren't very good. The stuff at hobby/craft stores are probably OK, although overpriced. Basically you want cabinet grade baltic (or finnish) birch plywood. These are solid without voids and all-around a good quality plywood. Sloan's is a good place to find plywood for scrollers. Ebay is another great place. You can check out our Wood Finder here on this site that lists plywood available on eBay. I buy mine from a lumber store that specializes in wood for cabinet/furniture makers.
A couple of other things that might help. You can use Blue Painter's tape on the bottom of your cutting as well. This will add extra support to the wood fibers and reduce tearout.
If you're working on delicate cutting, you may want to get a zero-clearance insert for your saw. This will close up the hole in the saw bed so your work is supported even better. I usually just poke a hole through a business card, thread my blade through it, then tape the card to my saw. You can also drill a hole through some plywood and tape that to your saw bed as well.
Anyway, there's a few ideas that might help. Please let us know if you run into problems. It is a very rewarding hobby that will impress your friends. Welcome to the hobby!