  A calculation of the ratio of leptonic decay constants f_{K^+}/f_{\pi^+}
makes possible a precise determination of the ratio of CKM matrix elements
|V_{us}|/|V_{ud}| in the Standard Model, and places a stringent constraint on
the scale of new physics that would lead to deviations from unitarity in the
first row of the CKM matrix. We compute f_{K^+}/f_{\pi^+} numerically in
unquenched lattice QCD using gauge-field ensembles recently generated that
include four flavors of dynamical quarks: up, down, strange, and charm. We
analyze data at four lattice spacings a ~ 0.06, 0.09, 0.12, and 0.15 fm with
simulated pion masses down to the physical value 135 MeV. We obtain
f_{K^+}/f_{\pi^+} = 1.1947(26)(37), where the errors are statistical and total
systematic, respectively. This is our first physics result from our N_f = 2+1+1
ensembles, and the first calculation of f_{K^+}/f_{\pi^+} from lattice-QCD
simulations at the physical point. Our result is the most precise lattice-QCD
determination of f_{K^+}/f_{\pi^+}, with an error comparable to the current
world average. When combined with experimental measurements of the leptonic
branching fractions, it leads to a precise determination of |V_{us}|/|V_{ud}| =
0.2309(9)(4) where the errors are theoretical and experimental, respectively.
