We report on the first simultaneous observations of chromospheric "anemone" jets in solar active regions with the Hinode Solar Optical Telescope (SOT) Ca II H broadband filtergraph and the Ca II K spetroheliograph on the Domeless Solar Telescope (DST) at Hida Observatory. During the period of coordinated observations, nine chromospheric anemone jets were simultaneously observed with the two instruments. These observations revealed three important features: (1) the jets are generated in the lower chromosphere; i.e., these cannot be seen in Ca II K-3; (2) the length and lifetime of the jets are 0.4-5 Mm and 40-320s, respectively; (3) the apparent velocity of the jets observed with the SOT is 3-24 km s(-1), while the Ca II K-3 component at the jets shows a blueshift (in 5 events) in the range of 2-6 km s(-1). The chromospheric anemone jets are associated with mixed polarity regions, which are either small emerging flux regions or moving magnetic features. It is found that the Call K line often shows red or blue asymmetry in the K-2/K-1 component; the footpoint of the jets associated with emerging flux regions often shows a redshift (2-16 km s(-1)), while the one with moving magnetic features shows a blueshift (similar to 5 km s(-1)). A detailed analysis of the magnetic evolution of the jet-forming regions revealed that the reconnection rate (or canceling rate) of the total magnetic flux at the footpoint of the jets is on the order of 10(16) Mx s(-1), and the resulting magnetic energy release rate is (1.1-10) x 10(24) erg s(-1), with a total energy release of (1-13) x 10(26) erg for the duration of the magnetic cancellation, similar to 130s. These are comparable to the estimated total energy, similar to 10(26) erg, in a single chromospheric anemone jet. In addition to the DST Call K spectroheliogram and the SOT Ca II H broadband filtergram, we also used for analysis an SOT magnetogram as well as a Hida Ha filtergram. We present a physical model of the jet based on the observation, and discuss the relation between chromospheric anemone jets and Ellerman bombs.