An element and a vial transport assembly made of a plurality of elements pivotally joined together to form a unitary row for storing and transporting vials and other such containers is disclosed. The assembly comprises a vial gripper removably seated on an inner face of the element. The unitary row of elements may be pivoted together to a closed position to secure the vials therein, and in some embodiments includes complementary magnets arranged to secure adjacent elements in registration when in the closed position.