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