We present evidence for jet-like X-ray-emitting features from the nearby pulsar, B2224+65, based on three epochs of Chandra X-ray observations, separated by 6 years from each other. This relatively slow rotating pulsar is well known for its extreme velocity of proper motion and associated “Guitar”-shaped optical nebula in the opposite direction. The main jet-like X-ray-emitting feature is extremely narrow and significantly curved near the pulsar, but further away remains amazingly straight and is directed about 62 degrees away from the nebula, the X-ray emission of which is also detected. We find the consistent proper motions of the pulsar and the feature. The substructure of the feature varies among the epochs, while its spectrum is well characterized by a power law with a photon index of 1.2, is significantly harder than that of the pulsar, and remains remarkably consistent spatially and with the time. These results can be explained most intuitively by ballistic, relativistic, and probably magnetic field-dominated jets from the pulsar, similar to those from active galactic nuclei. Indeed, we also detect the extended X-ray emission from the putative counter-jet, albeit at a much fainter level and on a much smaller scale. The luminosity of these features is 7e30 erg/s in the Chandra band, accounting for about 1% of the spin-down energy rate of the pulsar. Because of the flat nonthermal X-ray spectrum, this fraction increases with the photon energy. The total power required to generate the jets is likely greater than 10% of the rate. Much of the acceleration of the particles for the (synchrotron) X-ray emission to energies > 100 TeV likely occurs within the jets, probably via magnetic field re-connection. This jet scenario and the underlying physics can be further tested by a carefully designed X-ray monitoring of the substructure and by a measurement of the radio polarization of the pulsar, as its spin axis is expected to be aligned with the jets. We speculate that the energetic jet ejection from B2224+65 may represent a common phenomenon of pulsars, young and old, and an important source of cosmic-rays. The understanding of the ejection could also shed lights into the nature of extragalactic jets.