  (Abridged) We present spectroscopic and photometric observations of the
eclipsing system V1061 Cyg (P = 2.35 days). We show that it is a hierarchical
triple in which the third star is visible in the spectra. We combine the radial
velocities for the three stars, times of eclipse, and intermediate astrometric
data from the HIPPARCOS mission (abscissa residuals) to establish the elements
of the outer orbit (P = 15.8 yr) and accurate values for the masses and radii
(1-2% errors) and the effective temperatures of the binary components. Both
stars are rotating rapidly and have their rotation synchronized with the
orbital motion. There are signs of activity including strong X-ray emission and
possibly spots. Current stellar evolution models agree well with the properties
of the primary, but show a very large discrepancy in the radius of the
secondary: the predicted values are about 10% smaller than observed (a 5-sigma
effect). Also, the temperature is cooler than predicted by some 200 K. These
discrepancies are quite remarkable given that the star is only 7% less massive
than the Sun, the calibration point of all stellar models. We identify the
chromospheric activity as the likely cause of the effect. Inactive stars agree
very well with the models, while active ones such as V1061 Cyg Ab appear
systematically too large and too cool. Theory provides an understanding of this
in terms of the strong magnetic fields commonly associated with stellar
activity, which tend to inhibit convective heat transport.
