Invisibility devices have captured the human imagination for many years. Recent theories have proposed schemes for cloaking devices using transformation optics and conformal mapping. Metamaterials, with spatially tailored properties, have provided the necessary medium by enabling precise control over the flow of electromagnetic waves. Using metamaterials, the first microwave cloaking has been achieved but the realization of cloaking at optical frequencies, a key step towards achieving actual invisibility, has remained elusive. Here, we report the first experimental demonstration of optical cloaking. The optical `carpet' cloak is designed using quasi-conformal mapping to conceal an object that is placed under a curved reflecting surface by imitating the reflection of a flat surface. The cloak consists only of isotropic dielectric materials, which enables broadband and low-loss invisibility at a wavelength range of 1,400-1,800nm.