We used the Spitzer Space Telescope Infrared Spectrograph (IRS) to obtain mid-infrared (5-35 μm) spectra of two highly luminous B[e] stars in the Large Magellanic Cloud (LMC), R126 (HD 37974) and R66 (HD 268835). Both stars display flat spectra with silicate emission features; R66 displays, in addition, spectral evidence of crystalline grains and PAHs. Given the similarity of the IRS spectra of R126 and R66 to those of pre-main-sequence stars, we interpret these spectra as being due to thermal emission from circumstellar dust disks. Comparison with a model of thermal emission from a passive, irradiated dust disk suggests that the disks around R126 and R66 are quite massive, with ~3×10-3 Msolar of dust contained between 120 and 2500 AU from the star in the case of R126. Episodic mass ejections and/or debris disks (perhaps surrounding as-yet undetected companion stars) represent potential sources for the thermal dust emission from these and other B[e] hypergiants in the LMC.