A body area network is developed for a 3-Lead wireless electrocardiography (ECG) monitoring system. To measure the 3-Lead ECG signals without using wires for electrodes to connect to a common ground, we study a new ECG sensing method that directly and synchronously measures the voltage differences across the nearby electrodes of distributed ECG leads. To verify the effectiveness of the proposed method, the qualities of the ECG signals acquired from various placements and distances between the electrodes are compared with the ones obtained with the standard wired ECG measurement method. The highest correlation coefficient between the wired and wireless ones is shown by experiments to be as high as 0.946. And the separation between the two electrodes of an ECG lead can be drastically reduced to around 10cm which is about the size of a medium adhesive tape. This shows that a 3-Lead wireless ECG monitoring system is in fact feasible. More advanced approaches may be developed based on the results obtained herein to further construct a 12-Lead wireless ECG system.