We report experimental coupling of chiral magnetism and superconductivity in [IrFeCoPt]/Nb heterostructures. The stray field of skyrmions with radius ≈50 nm is sufficient to nucleate antivortices in a 25 nm Nb film, with unique signatures in the magnetization, critical current, and flux dynamics, corroborated via simulations. We also detect a thermally tunable Rashba-Edelstein exchange coupling in the isolated skyrmion phase. This realization of a strongly interacting skyrmion-(anti)vortex system opens a path toward controllable topological hybrid materials, unattainable to date.