I make a lot of pizza, about once a week, usually on the grill but also on pizza stone in the oven when it's cold out. I've gotten really good at it over the years, but I wish my dough was more chewy.

We got some pizza at a place the other night and the dough was perfect, it was thin, very chewy and nice and brown on the bottom.

I keep a big jar of red star yeast in the freezer, usually make a proof with a spoonful and a cup of warm water, then about 3 cups of flour, some salt and some Italian seasoning in the Kitchenaid with a dough hook, and just add the proof until it's the right consistency.

I usually do this in the morning and let it sit covered for the day, then just roll it out with a pin right before cooking. I usually get some good bubbles in it, and a good level of chewiness, but I want more. Ive tried kneading it again before cooking, but then I end up with too much density, more like a loaf of bread.

Do I need to let it sit longer to get some more gluten action? Should I knead it again halfway through the day?

Anyone that knows more about the science of yeast and flour have any suggestions?

I make my dough similar to you however I make it the night before and put it in the fridge. Are you using bread flour? Don't use rapid yeast if you are. Proof your yeast for 30 minutes prior to adding it to the flour.
Pm me if you have any other questions:)

Just gold seal flour, or whatever is on sale, probably should try out a bread flour.

I proof it 30 minutes until it's got a good fizz going.

I'll try the refrigerator thing next time and see what happens.

Try this recipe?
Best Pizza Dough Ever

I notice it uses high gluten flour. I think that is where I'm lacking what I want, I need more gluten in it to get that nice chewy quality.

Yup, get bread flour, make the night before and you will be golden.

Use bread flour (high protein) if you want a chewier crust, use AP flour if you want a crisper crust.
I use bread flour and let mine cold slow rise in the refrigerator for 3 to 4 days before I roll it out.

Info about flour for pizza here:
http://slice.seriouseats.com/archives/2011/06/the-pizza-lab-on-flour-foams-and-dough.html

Info about the rise here:
http://slice.seriouseats.com/archives/2010/09/the-pizza-lab-how-long-should-i-let-my-dough-cold-ferment.html

The secrets to the perfect pizza dough are a "00 or Caputo Flour" and a cold rise. Do not use bread flour. A cold rise using AP flour will be much better. Make sure that you knead or mix the dough, let it rest for a few minutes and then knead with a dough hook to further strengthen the gluten. My recipe has been posted here before as well as for quick dough.

eat the dough raw

I'd take a lead on Shakeys Pizza, pan dough.

Tag for useful tips

You need to cut way down on the yeast and cold ferment it for a few days if your making pizza dough the same day your eating it you're doing it wrong

Sorry, but I have to disagree.
I, like the OP, prefer a chewier crust.
00 or Caputo make excellent Neapolitan crispy crust (which is good if a crisp crust is what you want), but for a chewier crust as the OP wants he needs the higher protein flours like bread flour.

High gluten flour,cake yeast.
Put your salt in mixer,add your warm water,flour then yeast,mix for about 10 to 15 min on low.you want a shean on the dough weight it,knead into ball. put in reefer covered,best is for 2 to 3 days.you will see yeast spots on dough after 2 days.now make a pie.dough will stay good for about 2 days after it has risen.if you can'take find the flour at the store,try your local pizzeria ,they will probably sell ya a lb or two.

Bingo.  You need a proper high gluten flour.  King Arthur's aint bad.

High gluten flour

Been using this recipe for years..  I think it's the bread flour that does the trick.

Butter Herb, Basil Cheese Stuffed and Rosemary Garlic Pizza Crust
INGREDIENTS:
1 1/2 cups warm water
3 - 4 cups bread flour
1 teaspoon sea salt
1 package, or 2 1/2 teaspoons yeast
1 tablespoon honey
1/4 teaspoon garlic powder
1/4 teaspoon onion powderFor the Butter Herb Crust:
3 tablespoons melted butter
1 teaspoon dried Italian herbs (basil, oregano and rosemary), or 1 tablespoon fresh

For the Basil Stuffed Cheese Crust:
3 tablespoons olive oil
1 teaspoon dried basil, or 1 tablespoon fresh
about 6 pieces of mozzarella string cheese, torn in half lengthwise

For the Rosemary Garlic Crust:
3 tablespoons olive oil
1 teaspoon dried rosemary, or 1 tablespoon fresh

DIRECTIONS:Combine warm water, yeast, honey, salt, onion and garlic powder in your stand mixer. Mix until yeast dissolves. Add herbs (Italian blend, basil or rosemary) and butter or olive oil. Turn mixer to low and add flour until dough starts to pull away from bowl. Knead for about 10 minutes. Dough should be sticky and smooth. Grease a large metal bowl with olive oil. Form dough into a ball and transfer to bowl. Cover with plastic wrap and a towel. Let rise about 2 hours in a warm place, or until dough doubles in size. Punch down, from into a ball again and let rise again until it doubles in size.Preheat oven to it's highest temperature. For thin crust, divide dough in half and roll out pizza crust to the size of pizza pan or stone. For a thicker, traditional crust use all the dough and stretch out with hands and roll until it's the size of a large pizza pan.If you are stuffing the crust, place the string along the edges of the crust and roll the crust over the cheese, and seal the dough.Pre-bake crust in oven set at it's highest baking temperature (mine is 550°) until crust is lightly golden. Remove crust from oven.Spoon over pizza sauce (I use either a quality jarred pizza sauce or homemade). Layer cheese and your favorite toppings.Bake pizza again at your oven's highest temperature until cheese is lightly browned.Brush pizza crust with olive oil or butter after baking if desired.

Does this post have something in it? All I see is a blank post, with grey background. Chrome browser. Never had an issue before...

THIS!!!  Gluten is good stuff and good for you, unless you are a member of the roughly 1% of the population who can't digest it.

Gluten forms cross links given time. It makes it chewy. Rest the dough and use more gluten. cross linking happens more with wetter dough and shortening stops cross linking. Kneading more causes more crosslinking too

Bread flour crispier crust, All Purpose flour chewier crust.

Bread flour, or other higher protein flours, have more gliadin and glutenin, that combine through the process of kneading to form strands of gluten.  More gluten makes the dough chewier.

So, use a bread or pizza flour, and knead it prior to allowing it to rise, and maybe again after.  Allowing it to rise can also increase formation of gluten, thus the importance some people place on allowing a multi-day rise.