Thank you for the help btw. I swatted the moth into the abyss as well as all of the eggs I could find.
It is was actually zucchini sitting next to winter squash which also had eggs on it.
This is my first gardening project and going into it was well aware of the flaws in my set up so I expected to see stuff like this. Already dealt with hawkmoth larvae on my tomatoes and obliterated them with soapy water.
If that was the only one laying eggs you probably caught the problem in time BUT, if that is not the case here is how to fix the problem.
It takes about a week for the eggs to hatch and start their path of destruction. So during this week of incubating you should spray the entire squash plant with Neem Oil. This will smother the eggs. Next use a lot of Dipel dust up and down and around the base of the plant. This is where the hatched larvae will try to penetrate the stem of the plant, usually about 4 to 8 inches above soil level. Keep a close watch on this area. If you do see a hole form there is 2 things you can then do. The first is, I think, the safest thing. Get the largest hypodermic needle and syringe you can find and fill it up with Bt (Bacillus thuringensis) and shoot the bottom foot of the stem. Any caterpillar in there will soon be dead. Or second, you can get a sharp knife and split the stem open and try to find the caterpillar. Then cover up the damaged area with soil.