It is well-known that if $X$ is an integral scheme, then there is an isomorphism $CaCl(X)\to Pic(X)$ taking $[D]$ to $[\mathcal{O}\_X(D)]$. Does anyone know any simple examples where the above map fails to be surjective, i.e., a line bundle on a scheme $X$, not isomorphic to $\mathcal{O}\_X(D)$ for any Cartier divisor D? 



Line bundles vs. Cartier divisors on a non-integral scheme
An example is given in this [note](http://webs.uvigo.es/martapr/Investigacion/Divisors.pdf) (it was credited to Kleiman). 


