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We report the first microwave noise characterization of AlInN/GaN HEMTs. Transistors with a 0.1 μ m gate implemented on a semi-insulating SiC substrate achieve a maximum current density of 1.92 A/mm at VGS = 0 V, a measured transconductance gM = 480 mS/mm, and a peak current gain cutoff frequency fT = 121 GHz with a simultaneous maximum oscillation frequency fMAX = 142 GHz. At 10 (20) GHz, our HEMTs exhibit a minimum noise figure Fmin of 0.62 (1.5) dB together with a high associated gain GA of 15.4 (13.3) dB. The Fmin values are among the lowest reported in nitride HEMTs, and the GA values are the best so far found in the literature, demonstrating the excellent potential of AlInN/GaN HEMTs for low-noise microwave applications.