  In this paper, we define a class of 3-algebras which are called
3-Lie-Rinehart algebras. A 3-Lie-Rinehart algebra is a triple $(L, A, \rho)$,
where $A$ is a commutative associative algebra, $L$ is an $A$-module, $(A,
\rho)$ is a 3-Lie algebra $L$-module and $\rho(L, L)\subseteq Der(A)$. We
discuss the basic structures, actions and crossed modules of 3-Lie-Rinehart
algebras and construct 3-Lie-Rinehart algebras from given algebras, we also
study the derivations from 3-Lie-Rinehart algebras to 3-Lie $A$-algebras. From
the study, we see that there is much difference between 3-Lie algebras and
3-Lie-Rinehart algebras.
