We introduce stochastic time change to default intensity models of credit risk as a parsimonious way to account for stochastic volatility in credit spreads. We derive two series solutions for the survival probability function, and show that both methods are applicable when the intensity follows the widely-used basic affine process. This leads to straightforward and efficient solutions to bond prices and CDS spreads. We then estimate the time-changed model on panels of CDS spreads (across maturity and observation time) using Bayesian MCMC methods. We find strong evidence of stochastic time change. Co-authors are: Ovidiu Costin, Min Huang, and Pawel Szerszen.