  The far ultraviolet (FUV) continuum flux is recognized as a very sensitive
diag- nostic of the temperature structure of the Sun's lower chromosphere.
Until now analysis of the available stellar FUV data has shown that solar-type
stars must also have chromospheres, but quantitative analyses of stellar FUV
continua require far higher quality spectra and comparison with new non-LTE
chromosphere models. We present accurate far ultraviolet (FUV,
1150-1500^{\circ}) continuum flux measurements for solar-mass stars, made
feasible by the high throughput and very low detector background of the Cosmic
Origins Spectrograph (COS) on the Hubbble Space Telescope. We show that the
continuum flux can be measured above the detector background even for the
faintest star in our sample. We find a clear trend of increasing continuum
brightness temperature at all FUV wavelengths with decreasing rotational
period, which provides an important measure of magnetic heating rates in
stellar chromospheres. Comparison with semiempirical solar flux models shows
that the most rapidly rotating solar-mass stars have FUV continuum brightness
temperatures similar to the brightest faculae seen on the Sun. The thermal
structure of the brightest solar faculae therefore provides a first-order
estimate of the thermal structure and heating rate for the most rapidly
rotating solar-mass stars in our sample.
