Preheat the oven to 300°F.
Grease the sides of an 8 x 8 inch baking pan, then line the bottom and two opposite sides with a sheet of parchment paper, leaving an inch or two of overhang.
Stir the water and ground flaxseeds together in a large mixing bowl. Let the mixture sit for at least five minutes, to gel.
While the flax mixture sits, whisk the flour, cocoa powder, and salt together in a large mixing bowl. Set this aside for now.
Add the sugar, brown sugar, and vanilla to the bowl with the flax mixture. Use an electric mixer at high speed to beat the ingredients together for about 1 minute, until the mixture becomes slightly foamy.
Add the melted butter and briefly beat it into the flax mixture.
Begin adding the flour mixture to the bowl with the flax mixture, adding about a third at a time, and beating each addition in at low speed just until fully incorporated.
Fold the chocolate chips into the batter by hand.
Pour the batter into the prepared baking pan. Bake the brownies for 45 to 55 minutes, until the top is set and a toothpick inserted into the center of the brownies comes out clean.
Place the pan on a cooling rack and let the brownies cool completely.
Remove the brownies from the pan by gently pulling up on the excess parchment paper hanging over the pan.
Slice the brownies and serve.