How do I make oatmeal chocolate chip cookies that are thick?
Some keys to keeping cookies thick, beyond the chilled dough, are: use a starchier flour, use a fat with a high melting point, and use baking powder.

A starchier flour, like cake flour, will spread less than a flour that has higher protein, like all purpose. If you can't find cake flour, you could replace some of the flour in your recipe with a starch, like cornstarch or potato starch.

Shortening has a higher melting point than butter, replacing all or some of the butter in your recipe with shortening will allow the cookie to begin to set before the fat melts completely.

Finally, baking powder contains acids which help to keep the dough tighter. This helps it to "puff" more and spread less. If you can't use baking powder, you could add a bit of some other acidic ingredient to your dough (but cut the baking soda a bit as well or you might end up with cookies that are too cakey). A bit of a fruit vinegar, citrus juice, or cream of tartar would probably do the trick.