Transverse-field muon-spin rotation measurements in the vortex-lattice of the heavy-fermion (HF) superconductor PrOs4Sb12 yield a temperature dependence of the magnetic penetration depth lambda indicative of an isotropic or nearly isotropic energy gap. This is not seen to date in any other HF superconductor and is a signature of isotropic pairing symmetry, possibly related to a novel nonmagnetic "quadrupolar Kondo" HF mechanism in PrOs4Sb12. The T=0 relaxation rate sigma(s)(0)=0.91(1) micros(-1) yields an estimated magnetic penetration depth lambda(0)=3440(20) A, which is considerably shorter than in other HF superconductors.