We present spectroscopic and photometric observations of the chromospherically active (X-ray strong) eclipsing binary V1061 Cyg (P = 2.35 days) showing that it is in reality a hierarchical triple system. We combine these observations with Hipparcos intermediate data (abscissa residuals) to derive the outer orbit with a period of 15.8 yr. We determine accurate values for the masses, radii, and effective temperatures of the eclipsing binary components, as well as for the mass and temperature of the third star. For the primary we obtain M = 1.282 ± 0.015 M⊙, R = 1.615 ± 0.017 R⊙, Teff = 6180 ± 100 K, for the secondary M = 0.9315 ± 0.0068 M⊙, R = 0.974 ± 0.020 R⊙, Teff = 5300 ± 150 K, and for the tertiary M = 0.925 ± 0.036 M⊙ and Teff = 5670 ± 100 K. Current stellar evolution models agree well with the properties of the primary star, but show a large discrepancy in the radius of the secondary in the sense that the observed value is about 10% larger than predicted (a 5σ effect). We also find the secondary temperature to be ∼200 K cooler than indicated by the models. These discrepancies are quite remarkable considering that the secondary is only 7% less massive than the Sun, which is the calibration point of all stellar models. Similar differences with theory have been seen before for lower mass stars. We identify chromospheric activity as the likely cause of the effect. Inactive stars agree very well with the models, while active ones such as the secondary of V1061 Cyg appear systematically too large and too cool. Both of these differences are understood in terms of the effects of magnetic fields commonly associated with chromospheric activity.