We show that, in a Randall-Sundrum II type braneworld, the vacuum exterior of a spherical star is not in general a Schwarzschild spacetime, but has radiative-type stresses induced by five-dimensional graviton effects. Standard matching conditions do not lead to a unique exterior on the brane because of these five-dimensional graviton effects. We find an exact uniform-density stellar solution on the brane, and show that the general relativity upper bound GM/R<49 is reduced by five-dimensional high-energy effects. The existence of neutron stars leads to a constraint on the brane tension that is stronger than the big bang nucleosynthesis constraint, but weaker than the Newton-law experimental constraint. We present two different non-Schwarzschild exteriors that match the uniform-density star on the brane, and we give a uniqueness conjecture for the full five-dimensional problem.