Strong SiO masers occur in the inner regions of the stellar envelopes (within a few stellar radii) of variable late-type stars (Miras, semi-regular variables and supergiants), and in the vicinity of IRc2 in Orion, a site of recent star formation. Although linear polarization is a common feature of these masers1-3, previous attempts to detect circular polarization have been inconclusive. Johnson and Clark4 claimed detection of 10-20% polarization in Stokes V (left-hand circular minus right-hand circular) spectra of the Orion masers at 86.2 GHz. Troland et al.1 failed to confirm this result, while reporting small signals in Stokes V spectra for several sources which they attributed to instrumental effects. Here we report sensitive measurements of circular polarization in SiO masers associated with late-type stars, which reveal significantly polarized features at the several per cent level in five of six stars observed. Under the Zeeman splitting hypothesis, these measurements imply magnetic fields in the masing gas in the range 10-100 G. The masers associated with IRc2 in the Orion-KL region were not detected in circular polarization.