With an eye toward extending optical wave-mixing techniques to the x-ray regime, we present the first experimental demonstration of a two-color x-ray free-electron laser at the Linac Coherent Light Source. We combine the emittance-spoiler technique with a magnetic chicane in the undulator section to control the pulse duration and relative delay between two intense x-ray pulses and we use differently tuned canted pole undulators such that the two pulses have different wavelengths as well. Two schemes are shown to produce two-color soft x-ray pulses with a wavelength separation up to ∼1.9% and a controllable relative delay up to 40 fs.