Circular Rydberg states are ideal tools for quantum technologies, with huge mutual interactions and extremely long lifetimes in the tens of milliseconds range, two orders of magnitude larger than those of laser-accessible Rydberg states. However, such lifetimes are observed only at zero temperature. At room temperature, blackbody-radiation-induced transfers annihilate this essential asset of circular states, which have thus been used mostly so far in specific, complex cryogenic experiments. We demonstrate here, on a laser-cooled atomic sample, a circular state lifetime of more than one millisecond at room temperature for a principal quantum number 60. The inhibition structure is a simple plane-parallel capacitor that efficiently inhibits the blackbody-radiation-induced transfers. One of the capacitor electrodes is fully transparent and provides complete optical access to the atoms, an essential feature for applications. This experiment paves the way to a wide use of circular Rydberg atoms for quantum metrology and quantum simulation.