Final answer:
The nurse should stop the transfusion as the first action when a client reports chills and a headache after receiving packed red blood cells. They should then assess vital signs and notify the health care provider.
Step-by-step explanation:
When a client being transfused with one unit of packed red blood cells reports having chills and a headache within 15 minutes of the transfusion, the nurse should stop the transfusion as their first action. This is because these symptoms could indicate a transfusion reaction, which can be life-threatening. The nurse should then assess the client's vital signs and notify the health care provider for further guidance.