The design of new oxygen- and proton-conducting materials is of paramount importance for their possible utilization in solid oxide fuel cells. In the present work, La2(Hf2–xLax)O7–x/2 (x = 0, 0.1) ceramics were prepared using ball milling of oxide mixtures (La2O3 and HfO2) followed by high-temperature annealing at 1600 °C for 10 h in air. La2Hf2O7 ceramics exhibit an ordered pyrochlore-type structure, whereas La2(Hf1.9La0.1)O6.95 has a defect pyrochlore structure type with oxygen vacancies at the 48f positions. The oxygen ion and proton conductivity of La2(Hf1.9La0.1)O6.95 “stuffed” pyrochlore ceramics was investigated by electrochemical impedance spectroscopy (two-probe AC) and four-probe DC measurements in a dry and a wet atmosphere (air and nitrogen). The use of two distinct conductivity measurement techniques ensured, for the first time, the collection of reliable data on the proton conductivity of the La2(Hf1.9La0.1)O6.95 “stuffed” hafnate pyrochlore. La2Hf2O7 was found to be a dielectric in the range 400–900 °C, whereas the La2(Hf1.9La0.1)O6.95 “stuffed” pyrochlore had both oxygen ion and proton conductivities in this temperature range. The proton conductivity level was found to be equal to ~8 × 10−5 S/cm at 700 °C. Clearly, the proton conductivity of the La2(Hf1.9La0.1)O6.95 “stuffed” hafnate pyrochlore is mainly due to the hydration of oxygen vacancies at 48f positions.