We argue that the presence of an inflationary epoch is a natural, almost unavoidable, consequence of the existence of a sensible effective action involving an infinite tower of higher-curvature corrections to the Einstein-Hilbert action. No additional fields besides the metric are required. This correction to General Relativity has the following features: (i) its vacuum spectrum solely consists of a graviton and is ghost free, (ii) it possesses well-behaved black hole solutions, (iii) its cosmology is well-posed as an initial value problem and, most importantly, (iv) it has the potential to provide a late-time cosmology arbitrarily close to LCDM while, at the same time, giving an inflationary period in the early universe with a graceful exit