Consider a duration time $T$, a possibly endogenous covariate $Z$ and a vector of exogenous covariates $X$ such that $T=varphi(Z,X,U)$ is increasing in $U$ with $U sim U[0,1]$. Moreover, let $T$ be right-censored by a censoring time $C$ such that only their minimum, denoted by the follow-up time $Y=min{T,C}$, is observed. In this paper, we construct a test statistic for the hypothesis that $Z$ is exogenous w.r.t. $T$, where $T$, given $Z$ and $X$, is assumed to follow a proportional hazards model. Note that this is equivalent to testing whether $U$ is independent of $Z$. Our test makes use of an instrumental variable $W$ that is independent of $U$, since it can be shown that $Z$ is exogenous w.r.t. $T$ if and only if $V_T = F_{T mid Z,X}(T mid Z,X)$ is independent of $W$. We prove some asymptotic properties of the proposed test, provide possible bootstrap approximations for the critical value and show that we have a good finite sample performance via simulations. Lastly, we give an empirical example using The National Job Training Partnership Act (JTPA) Study.