scott is right. When it comes to achieving chewiness in a NY style crust there is a fairly fine line between chewy and tough. So, some experimentation will normally be required to achieve the degree of chewiness you are after, especially in a home setting where there are so many variables. The most typical ways that chewiness in a baked crust is achieved are as follows, pretty much in the order noted:
1) Use a high gluten flour, such as the King Arthur Sir Lancelot or comparable brand. The high protein content of such flours inherently contributes to chewiness and is one of the reasons high gluten flours are so often used by pizza operators to make NY style pizzas. If only bread flour or all-purpose flour are available, then vital wheat gluten (VWG) can be added to such flours, following the recommended amounts/rates specified by the producer of the VWG.
2) Add semolina flour to the base flour selected. A typical range is up to about 25% of the total flour (by weight), although one pizza operator I spoke with who makes a semolina-based NY style uses about 50%. A crust using semolina flour will sometimes start out being a bit crispier but as it sets it becomes chewier. Some people use cornmeal instead of semolina flour, but cornmeal imparts a distinctive flavor component that isn't nearly as noticeable as when using semolina flour and may not be desirable. Cornmeal may also produce some grittiness in the crust, which may also not be desired.
3) Slightly underbake the pizza, provided this can be done such that the top and bottom of the pizza are done at the same time. You might be able to compensate in part by using the broiler element in your oven to finish the top of the pizza before the crust dries out and becomes too crispy.
4) Reduce the hydration (the weight of water relative to the weight of flour) and/or reduce the amount of oil and/or sugar, both of which tend to impart softness and tenderness to the crumb when used at levels that exceed around 4-5%. Some NY style dough recipes are already light on the oil and sugar, so in such cases there is little that needs to be done. However, some NY style dough recipes call for a fair amount of oil and/or sugar. Reducing the amounts of those ingredients should contribute to chewiness. Some care is required in changing the levels of water, oil and sugar, especially in the case of the hydration, since you may end up with a tough crust rather than a chewy one.
5) Allow a finished pizza to rest for a few minutes directly on a flat surface rather than on a rack. This forces steam back into the pizza crust and can increase the chewiness. However, there is an equal chance that you will also get a somewhat softer crust.
Another approach to achieving increased chewiness that is rarely mentioned but provides a nice degree of chewiness in my opinion is to use a preferment as the leavening agent for the dough. Doing this produces a sourdough type of crumb that has a high degree of stretchiness and elasticity at the same time. You can tug and pull the crust and see the strands of the crumb stretch but not break. They just spring back when you release the crust. These qualities inherently contribute to the chewiness of the crust. A nice side benefit of such a crust is that the chewiness remains in any leftover slices (if you have any). That is because a sourdough-based crust has better keeping qualities than most crusts made with commercial yeast with a dramatically lowered staling rate.
If you find a solution that works best for you, I hope that you will report back to us on your results since many of our members may also be looking for a chewier NY style crust.