Transmission electron microscopy studies of the perovskite NaLaMgWO6 reveal the formation of a complex, compositionally modulated structure. Annular dark field scanning transmission electron microscopy images and scanning transmission electron microscopy-electron energy-loss spectroscopy scans show that this modulation involves a repeating pattern of La-rich and La-poor stripes, each stripe 6a(p) or similar to 24 angstrom wide (where a(p) is the edge length of the simple cubic perovskite unit cell). High-resolution transmission electron microscopy images clearly show, and electron diffraction patterns confirm, a periodicity of 12a(p) along either the [100](p) or [010](p) direction. Available evidence suggests a spontaneous separation into stripes that possess the nominal stoichiometry, NaLaMgWO6, alternating with Na-poor/La-rich stripes that have a stoichiometry of (LaxNa1-3x)LaMgWO6. X-ray powder diffraction measurements are insensitive to this intricate structural complexity, which may be a more widespread feature of (A(+)Ln(3+))MM'O-6 perovskites than previously appreciated.