Peg-in-hole insertion is not only a longstanding problem in robotics but the most common automated mechanical assembly task. In this paper we present a high precision, self-calibrating peg-in-hole insertion strategy using several very simple, inexpensive, and accurate optical sensors. The self-calibrating feature allows us to achieve successful dead-reckoning insertions with tolerances of 25 microns without any accurate initial position information for the robot, pegs, or holes. The program we implemented works for any cylindrical peg, and the sensing steps do not depend on the peg diameter, which the program does not know. The key to the strategy is the use of a fixed sensor to localize both a mobile sensor and the peg, while the mobile sensor localizes the hole. Our strategy is extremely fast, localizing pegs as they are in route to their insertion location without pausing. The result is that insertion times are dominated by the transport time between pick and place operations.