The pricing model for a First-to-Default (FtD) Credit Default Swap (CDS) with three assets is constructed with the assumptions that the default barrier is changing over time, the survival probability is log-normally distributed, and the default-free interest rate is constant. We calibrate the nonlinear dependence structure in the joint survival function of these assets by applying elliptical and Archimedean copula functions. There are two parts in the empirical study. First, we estimate the prices of the CDS of 30 firms that compose the Dow Jones Industrial Index using the model with a single asset and find that the estimated prices are not significantly different from the market prices. Second, we estimate the CDS price of a portfolio that consists of AT&T, Microsoft and Coca-Cola using the pricing model we constructed. Results show that the dependence among these firms can be better described by Gumbel copula functions.