I like my chocolate chip cookies chewy too
and I do it all the time.
Here is what I do: Flour:
I use a higher gluten flour instead of AP, such as Bread flour.
Eggs:
An additional egg yolk will help Sugar:
A bigger Brown Sugar to Sugar ratio helps but not vital if you do not have brown sugar at hand.
Butter:
Butter should be melted.
I think this is the key to chewiness.
The recipe is straightforward: cream butter with sugar, add wet ingredients, incorporate dry ingredients slowly and lastly add the chips.
Be sure to chill the dough for at least 30 min.
The more you rest, the better.
See this NY Times Article for effects of resting the dough.
cooking.stackexchange.com/users/207/Recep
This is the recipe for chocolate chip
cookiesFor more details check out the Jan/Feb 96 edition of Cooks Illustrated.
2 c. all-purpose flour plus two tablespoons more ½ t baking soda ½ t salt 1½ sticks Butter (melted and this is key!
also this is a bit less than typical) ½ c granulated sugar 1 c packed brown sugar 2 t vanilla extract 2 Eggs (1 whole, 1 yolk) 1 12oz (bag) semi-sweet chocolate chips Combine flour, baking soda, and salt in a small bowl.
Mix butter,granulated sugar, brown sugar, and vanilla in large mixer bowl.
Addeggs, one at a time, beating well after each addition;
gradually beatin flour mixture.
Stir in morsels and nuts.
Bake on un-greased cookiesheets for 15-18 min.
@
325°F.
Also this recipe works great with white whole wheat flour as well to add at least some nutrition.
I have had excellent success substituting 2 tablespoons of ground flax seed meal and 5 tablespoons of water for the eggs if you need to go egg-less.
cooking.stackexchange.com/users/419/John Dyer
In addition to what everyone else has said (increase fat...), make sure you let the dough rest (in the fridge or freezer) for at least 20 minutes before baking.
cooking.stackexchange.com/users/86/Shog9
More fat generally makes softer cookies.
For a great desciption of how the fat / sugar / flour ratio affects the texture of cookies etc.
check out Michael Ruhlman's "Ratio" cookbook.
cooking.stackexchange.com/users/46/Foodie Ron
You could try cooking at a slightly lower temperature, spraying the walls of your oven with water or putting an oven-safe bowl of water in with the cookies to prevent drying out, and/or cook them for less time.
When finished cooling immediately put them into an airtight container or foil and they will stay fairly soft, but of course are best just after cooling.
cooking.stackexchange.com/users/37/Daniel
You can do a number of things like using brown sugar instead of white, use more leavening, and use oil or margarine instead of butter.
cooking.stackexchange.com/users/40/Tesserex
On the Serious Eats Food Lab, J. Kenji Lopez Alt goes deep into
The Science of the Best Chocolate Chip Cookies .
He discusses a couple ideas for making your cookies chewier.
Use bread flour instead (or something with a higher protein content than your recipe calls for) Replace some sugar with a touch of corn syrup.
The higher protein content in the bread flour than in AP flour will lead to a chewier cookie.
The bread flour reference comes from The Chewy by Alton Brown.
cooking.stackexchange.com/users/52528/Caleb
I bake mine a minute or two less than it calls for and only let them cool half way and then place them in my cookie container with a layer of parchment paper between each layer and while still slightly warm cover tightly and
the heat of cookies will keep them from getting hard and will stay softer and chewier.
cooking.stackexchange.com/users/18771/Tracy Michaud
I have had brilliant results using this recipe that incorporates instant vanilla pudding mix.
These cookies come out with an incredible texture that you just want to keep putting your teeth inside, aside from the fact that they also taste incredible.
cooking.stackexchange.com/users/18791/KRA2008
You can also put a piece of white bread in your container with the cookies, as it will help keep the cookies softer for a longer time.
I don't know why, but it does work for me.
cooking.stackexchange.com/users/22856/user22856
The best way is a mix of both white and brown sugar.
Too much white and they'll be tough too much brown and they can break by their own weight.
Play with the two proportions till you find what you want.
More brown typically more chewy.
Another way is to make it with brown and to cool the dough in the fridge before baking so that the integrity is better.
cooking.stackexchange.com/users/66642/Jade So
My chocolate chips cookies are always too crisp. How can I get chewy cookies, like those of Starbucks?   Thank you to everyone who has answered. So far the tip that had the biggest impact was to chill and rest the dough, however I also increased the brown sugar ratio and increased a bit the butter. Also adding maple syrup helped.
How can I get chewy chocolate chip cookies?
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<baking><cookies><texture>
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cooking.stackexchange.com/users/16/Wizard79
Use a higher gluten flour, more fat, oil/margerine instead of butter, brown sugar or a mixture instead of just white, more leavening, or try a recipe using vanilla pudding. Chill the dough for 30 minutes before baking, spray water in the oven or place an oven-safe bowl of water in with the cookies. Cook at a lower temperature or for a minute or two less than the recipe calls for, then store in an airtight container when cool, possibly separated into layers or with a slice of bread in the container. A higher fat content or flour with increased gluten will make softer cookies. Make sure you chill the dough before baking. You can also try baking them at a lower temperature or for a shorter time. 
In general, a higher fat content will make softer cookies. You can try using brown sugar instead of white or a mix of the two. You can also try using flour with a higher gluten content. Instant pudding mix is also a good tip. Make sure you chill the dough before baking. Try cooking at a lower temperature or for a shorter amount of time. You can also put them into the container while still slightly warm and add a slice of white bread to keep them soft.