Due to high density of native defects, the prototypical topological insulator (TI), Bi2Se3, is naturally n-type. Although Bi2Se3 can be converted into p-type by substituting 2+ ions for Bi, only light elements such as Ca have been so far effective as the compensation dopant. Considering that strong spinorbit coupling (SOC) is essential for the topological surface states, a light element is undesirable as a dopant, because it weakens the strength of SOC. In this sense, Pb, which is the heaviest 2+ ion, located right next to Bi in the periodic table, is the most ideal p-type dopant for Bi2Se3. However, Pb-doping has so far failed to achieve p-type Bi2Se3 not only in thin films but also in bulk crystals. Here, by utilizing an interface engineering scheme, we have achieved the first Pb-doped p-type Bi2Se3 thin films. Furthermore, at heavy Pb-doping, the mobility turns out to be substantially higher than that of Ca-doped samples, indicating that Pb is a less disruptive dopant than Ca. With this SOC-preserving counter-doping scheme, it is now possible to fabricate Bi2Se3 samples with tunable Fermi levels without compromising their topological properties.