We construct a consistent supersymmetric action for chiral and vector multiplets living on codimension-two branes in a six-dimensional chiral gauged supergravity. A nonzero brane tension can be compatible with the bulk supersymmetry by introducing a brane-localized Fayet-Iliopoulos term proportional to the brane tension. Moreover, we show that a brane chiral multiplet with nonzero R charge has a nontrivial coupling to the extra component of the U(1)_R gauge field strength and a singular scalar self-interaction term. We find that a unwarped football solution with 4D Minkowski vacuum exists for arbitrary brane tension and it preserves 4D N=1 supersymmetry. Dimensionally reducing to 4D for the football solution, we obtain the low energy action for moduli and brane multiplets in 4D effective supergravity with gauged U(1)_R. By assuming the bulk gaugino condensates as well as nonzero brane F- and/or D-term for the uplifting potential, we have all the moduli stabilized with a vanishing cosmological constant. The brane scalar with nonzero R charge then gets a soft mass of order the gravitino mass, the sign of which depends on the sign of the R charge as well as whether the brane F- or D-term dominates.