(abridged) CIT 3 is an oxygen-rich long-period variable evolving along the AGB and one of the most extreme infrared AGB objects. We present the first bispectrum speckle-interferometry observations of CIT 3 in the J-, H-, and K-band (resolution: 48mas, 56mas, and 73mas). The interferograms were obtained with the Russian SAO 6m telescope. While CIT 3 appears almost spherically symmetric in the H- and K-band, it is clearly elongated in the J-band along a symmetry axis of position angle -28 degr. Two structures can be identified: a compact elliptical core (eccentricity ~0.8) and a fainter north-western fan-like structure (full opening angle ~40 degr). Extensive radiative transfer calculations have been carried out and confronted with the spectral energy distribution, our 1.24, 1.65 and 2.12 micron visibility functions, and 11micron ISI interferometry. The best model refers to a cool central star (Teff=2250K) surrounded by an optically thick dust shell (tau_V = 30). The central-star diameter is 10.9mas and the inner dust shell diameter 71.9mas. The inner dust-shell rim is located at r_1=6.6 Rstar and has a temperature of T_1=900K. A two-component model existing of an inner uniform-outflow shell region (rho~1/r^2; r < 20.5 r_1) and an outer region with rho ~ 1/r^1.5 proved to give the best overall match of the observations. Provided the outflow velocity kept constant, the more shallow density distribution in the outer shell indicates that mass-loss has decreased with time in the past of CIT 3. Adopting vexp=20km/s, the termination of that mass-loss decrease and the begin of the uniform-outflow phase took place 87yr ago. The present-day mass-loss rate can be determined to be Mdot = (1.3-2.1) x 10^-5 Msol/yr for d=500-800pc.
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