We present new neutral hydrogen (H I) observations of the nearby galaxy NGC 2403 to determine the nature of a low-column-density cloud that was detected earlier by the Green Bank Telescope. We find that this cloud is the tip of a complex of filaments of extraplanar gas that is coincident with the thin disk. The total H I mass of the complex is 2 × 107 M⊙ or 0.6% of the total H I mass of the galaxy. The main structure, previously referred to as the 8 kpc filament, is now seen to be even more extended, along a 20 kpc stream. The kinematics and morphological properties of the filaments are unlikely to be the result of outflows related to galactic fountains. It is more likely that the 20 kpc filament is related to a recent galaxy interaction. In this context, a ∼50 kpc long stellar stream has recently been detected connecting NGC 2403 with the nearby dwarf satellite DDO 44. Intriguingly, the southern edge of this stream overlaps with the tip of the 20 kpc H I filament. We conclude that the H I anomalies in NGC 2403 are the result of a recent (∼2Gyr) interaction with DDO 44 leading to the observed filamentary complex.