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We report on a continuous-time rigid-body pose estimator for a walking hexapod robot. Assuming at least three legs remain in ground contact at all times, our algorithm uses the outputs of six leg-configuration sensor models together with a priori knowledge of the ground and robot kinematics to compute instantaneous estimates of the 6-degrees-of-freedom (6-DOF) body pose. We implement this estimation procedure on the robot RHex by means of a novel sensory system incorporating a model relating compliant leg member strain to leg configuration delivered to the onboard CPU over a customized cheap high-performance local wireless network. We evaluate the performance of this algorithm at widely varying body speeds and over dramatically different ground conditions by means of a 6-DOF vision-based ground-truth measurement system (GTMS). We also compare the odometry performance to that of sensorless schemes - both legged as well as on a wheeled version of the robot - using GTMS measurements of elapsed distance.