We study with unprecedented detail the chemical composition and stellar parameters of the solar twin 18 Sco in a strictly differential sense relative to the Sun. Our study is mainly based on high-resolution (R ~ 110,000), high signal-to-noise ratio (800-1000) Very Large Telescope UVES spectra, which allow us to achieve a precision of about 0.005 dex in differential abundances. The effective temperature and surface gravity of 18 Sco are T_eff_= 5823+/-6 K and log g = 4.45+/-0.02 dex, i.e., 18 Sco is 46+/-6 K hotter than the Sun and log g is 0.01+/-0.02 dex higher. Its metallicity is [Fe/H] = 0.054+/-0.005 dex, and its microturbulence velocity is +0.02+/-0.01 km/s higher than solar. Our precise stellar parameters and differential isochrone analysis show that 18 Sco has a mass of 1.04+/-0.02 M_{sun}_ and that it is ~1.6 Gyr younger than the Sun. We use precise High Accuracy Radial velocity Planet Searcher (HARPS) radial velocities to search for planets, but none are detected. The chemical abundance pattern of 18 Sco displays a clear trend with condensation temperature, thus showing higher abundances of refractories in 18 Sco than in the Sun. Intriguingly, there are enhancements in the neutron-capture elements relative to the Sun. Despite the small element-to-element abundance differences among nearby n-capture elements (~0.02 dex), we successfully reproduce the r-process pattern in the Solar System. This is independent evidence for the universality of the r process. Our results have important implications for chemical tagging in our Galaxy and nucleosynthesis in general.