After performing the first set of 30 chest compressions on an unconscious choking person and confirming that emergency services have been called, the next step is to check the mouth for an object. If an object is visible and easily reachable, you can attempt to remove it. If it is not visible, you would proceed with the basic life support protocols, which typically include giving 2 rescue breaths, followed by more chest compressions.
However, always refer to the specific guidelines of the organization (like the American Heart Association) you are following, as practices can vary. In general, after checking the mouth and providing breaths if appropriate, you would continue with cycles of compressions and breaths.