We present the design, implementation, and evaluation of a multi-sensor low-power necklace NeckSense for automatically and unobtrusively capturing fine-grained information about an individuals eating activity and eating episodes, across an entire waking-day in a naturalistic setting. The NeckSense fuses and classifies the proximity of the necklace from the chin, the ambient light, the Lean Forward Angle, and the energy signals to determine chewing sequences, a building block of the eating activity. It then clusters the identified chewing sequences to determine eating episodes. We tested NeckSense with 11 obese and 9 non-obese participants across two studies, where we collected more than 470 hours of data in naturalistic setting. Our result demonstrates that NeckSense enables reliable eating-detection for an entire waking-day, even in free-living environments. Overall, our system achieves an F1-score of 81.6% in detecting eating episodes in an exploratory study. Moreover, our system can achieve a F1-score of 77.1% for episodes even in an all-day-around free-living setting. With more than 15.8 hours of battery-life NeckSense will allow researchers and dietitians to better understand natural chewing and eating behaviors, and also enable real-time interventions.