General conservation laws and symmetries permit one photon to split into three all traveling in the original direction. But QED predicts that this process has vanishing probability. Observations of the 3-K microwave background and optical line spectra of quasars can be used to test this over cosmic length scales. We discuss photon splitting within the framework of a Lorentz-covariant, phenomenological theory. This theory predicts (a) spectral broadening, (b) frequency-dependent red-shift, and (c) multiple red-shifts for each source. Because these effects do not show up, we can set observational limits on the parameters that govern the splitting. In particular, the 3-K background implies that a photon of arbitrary wavelength $\lambda$ propagating in flat space (i.e., without cosmological reddening) must have a decay lifetime larger than $\left(6\mathrm{} \frac{\mathrm{cm}}{\lambda }\right)t$, where $t$ is the present age of the universe.

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