We present a model for cosmological inflation based on a no-scale supergravity sector with an SUð2; 1Þ=SUð2Þ Â Uð1Þ Kähler potential, a single modulus T, and an inflaton superfield È described by a Wess-Zumino model with superpotential parameters (, ). When T is fixed, this model yields a scalar spectral index n s and a tensor-to-scalar ratio r that are compatible with the Planck measurements for values of ' =3M P . For the specific choice ¼ =3M P , the model is a no-scale supergravity realization of the R þ R 2 Starobinsky model. The initial release of cosmic microwave background data from the Planck satellite [1] confronts theorists of cosmological inflation [2,3] with a challenge. On the one hand, the data have many important features that are predicted qualitatively by the inflationary paradigm. For example, there are no significant signs of non-Gaussian fluctuations or hints of nontrivial topological features such as cosmic strings, and the spectrum of scalar density perturbations exhibits a significant tilt: n s '0:960AE0:007, as would be expected if the effective scalar energy density decreased gradually during inflation. On the other hand, many previously popular field-theoretical models of inflation are ruled out by a combination of the constraint on n s and the tensor-to-scalar ratio r < 0:08 as now imposed by Planck et al: see, e.g., Fig. 1 [5] and related models [6].In the following paragraphs we motivate the approach to inflation taken in this Letter, which casts a new light on the Starobinsky model [4] and embeds it in a more general theoretical context that connects with other ideas in particle physics. Specifically, the upper limit on r implies that the energy scale during inflation must be much smaller than the Planck energy, $10 19 GeV. Such a hierarchy of energy scales can be maintained naturally, without fine-tuning, in a theory with supersymmetry [7]. As is well known, (approximate) supersymmetry has many attractive features, such as providing a natural candidate for dark matter and facilitating grand unification, as well as alleviating the fine-tuning of the electroweak scale. In the context of early-universe cosmology, one must combine supersymmetry with gravity via a suitable supergravity theory [8], which should accommodate an effective inflationary potential that varies slowly over a large range of inflaton field values. This occurs naturally in a particular class of supergravity models [9], which are called ''no scale'' because the scale at which supersymmetry is broken is undetermined in a first approximation, and the energy scale of the effective potential can be naturally much smaller than $1019 GeV, as required by the cosmic microwave background data. No-scale models have the additional attractive feature that they arise in generic four-dimensional reductions of string theory [10], though this does not play an essential role in our analysis. The attractive features of this no-scale supergravity framework for inflation do not depend sensitively on the supersymmetry-breaking scale, w...