Precise manipulation of nanometer-sized magnetic particles using magnetic tweezers has yielded insights into the rheology of the cell cytoplasm. We present first results using this approach to study the nanomechanics of the cell nucleus. Using a custom-designed micro-magnetic-tweezers instrument, we can achieve sufficiently high magnetic forces enabling the application and measurement of controlled distortion of the internal nuclear structure on the nanometer scale. We precisely measure the elasticity and viscosity inside the nucleus of living HeLa cells. The high value of the Young's modulus (γ = 2.5 × 102 Pa) measured relative to the cytoplasm is explained by a large-scale model for in vivo chromatin structure using a polymer network model.