Staircase codes, a new class of forward-error-correction (FEC) codes suitable for high-speed optical communications, are introduced. An ITU-T G.709-compatible staircase code with rate $R=239/255$ is proposed, and field-programmable-gate-array-based simulation results are presented, exhibiting a net coding gain of 9.41 dB at an output error rate of $10^{-15}$ , an improvement of 0.42 dB relative to the best code from the ITU-T G.975.1 recommendation. An error floor analysis technique is presented, and the proposed code is shown to have an error floor at $4.0 \times 10^{-21}$.