Cut chicken breasts into 1-inch-thick strips. Set aside.

Stir together 1 cup flour and baking powder in a medium bowl. Mix in eggs and cold beer until combined. Place remaining 1/2 cup flour in a small bowl.

Heat oil in a deep heavy skillet to 375 degrees F (190 degrees C).

Working in batches, coat chicken strips in flour, then dip into beer batter. Fry chicken in hot oil, turning once, until chicken is no longer pink in the center and the coating is golden brown. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Drain on a paper towel-lined plate.