Measurements of the London penetration depth Δλ(T) and tunneling conductance in single crystals of the recently discovered stoichiometric iron-based superconductor CaKFe4As4 (CaK1144) show nodeless, two-effective-gap superconductivity with a larger gap of about 6–10 meV and a smaller gap of about 1–4 meV. Having a critical temperature Tc,onset≈35.8 K, this material behaves similar to slightly overdoped (Ba1−xKx)Fe2As2 (e.g., x=0.54,Tc≈34 K), a known multigap s± superconductor. We conclude that the superconducting behavior of stoichiometric CaK1144 demonstrates that two-gap s± superconductivity is an essential property of high-temperature superconductivity in iron-based superconductors, independent of the degree of substitutional disorder.