Preheat oven to 350ºF. Butter and flour a baking sheet; set aside.
In a medium bowl, whisk together flour, cocoa powder, baking soda, and salt. In the bowl of an electric mixer fitted with the whisk attachment, cream butter and sugar until light and fluffy. Add eggs; beat until well combined, scraping down sides of bowl if necessary. Add flour mixture, and stir to form a stiff dough. Stir in pistachios and chocolate chips.
Transfer dough to prepared baking sheet; form into a slightly flattened log, about 12 x 4 inches. Bake until slightly firm, about 25 minutes. Cool on a wire rack for about 5 minutes. Reduce oven temperature to 300ºF.
On a cutting board, using a sharp serrated knife, cut biscotti diagonally into 1-inch-thick slices. Arrange biscotti, cut sides down, on baking sheet, and bake until crisp but still slightly soft in the center, about 8 minutes.
