General relativity predicts that standard clocks placed at differing gravitational potentials will run at different rates. Although experiments confirming the gravitational redshift have been done, they involve frequency and not time, and need not appeal to general relativity for explanation. Therefore, considerable interest exists as to the result of an accurate experiment in which real macroscopic clocks are brought together for comparison before and after separation to differing potentials. This experiment consists of flying an ensemble of atomic clocks in a military aircraft and comparing them before and after flight to another clock ensemble remaining on the ground. The ground ensemble included several Hewlett-Packard Cesium Beam clocks, three Efratom optically pumped Rubidium clocks, and two hydrogen masers. The flying ensemble included at least three Hewlett-Packard Cesium clocks and three Efratom Rubidium clocks. Five of the Cesium clocks were new models delivered with a high beam current option resulting in higher stability than standard models. The clocks were maintained under stringent environmental controls to protect against vibration, magnetic fields, and changes in temperature, pressure, and power supply voltage. Five main flights were ma de, each at approximately 30,000 feet altitude for fifteen hours. The aircraft was continuously tracked by a theodolite calibrated radar which obtained position and velocity measurements for every second of flight. This allowed an accurate calculation of a theoretical prediction to compare to experiment. The flying clocks gained approximately 45 nanoseconds (45 x 10-9 s) with respect to the ground clocks. The normalized results (measured effect divided by predicted effect) and the experimental standard deviations of the mean for each of the five flights were as follows: .999 + .016 .977 + .026 .963 + .013 1.002 + .026 .991 + .037 The result for the entire experiment, with standard deviation of the mean, was .987 ±. .011. The statistically expected standard deviation of the mean based on knowledge of clock quality was approximately .015. Considering this result as well as systematic errors, a final result is established of Measured value/ Predicted value = 0.987 ± .016