The half-life of Ca-38, a T-Z = -1 superallowed 0(+) -> 0(+) beta(+) emitter, has been measured to be 443.77(36) ms. In our experiment, pure sources of 38Ca were produced and the decay positrons were detected in a high-efficiency 4 pi proportional gas counter. Since the beta(+) decay of Ca-38 feeds K-38(m), which is itself a superallowed beta(+) emitter, the data were analyzed as a linked parent-daughter decay. Our result, with a precision of 0.08%, is a factor of 5 improvement on the best previous result.