Preheat the oven to 375 degrees F and line rimmed baking sheets with parchment paper.
Add the flour, baking soda and salt to a medium bowl and whisk to combine; set aside.
In a large bowl, cream the butter and sugars together with mixer until lighter in color and fluffy, 1 to 2 minutes, scraping down the bowl as needed.
Add the egg and beat until incorporated. Add the lemon zest, lime zest and vanilla extract. Beat until evenly combined.
Add dry ingredients to the butter-sugar mixture and mix until just incorporated. Fold the chocolate chips in with a rubber spatula.
Use a 1-tablespoon cookie scoop to scoop the cookie dough onto the prepared baking sheets, keeping them 2 inches apart.
Bake until edges are golden brown and the centers are still soft, 8 to 10 minutes.
Allow the cookies to cool on the baking sheets for 5 minutes, then transfer them to a wire rack to cool completely.
Repeat the process with the remaining dough. Alternatively, the cookie dough can be wrapped in plastic wrap and frozen up to a month.