Ground state laser cooling of a single trapped Ca(+)on is achieved with a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency. Using the Zeeman structure of the S(1/2) to P(1/2) dipole transition we achieve up to 90% ground state probability. The new method is robust, easy to implement, and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions.