First result of experiment for searching of 2 K -capture of 124 Xe with the large-volume copper proportional counter (LPC) is given. The 12 liters sample with 63.3% (44 g) of 124 Xe was used in measurements. The limit on the half-life of 124 Xe with regard to 2 K (2ν)-capture for the ground state of 124 Te (0 + → 0 + , g.s.) has been found: T 1/2 ≥ 4.67 × 10 20 yr (90% C.L.). A sample with volume 52 liters comprising of 124 Xe (10.6 L - 58.6 g) and 126 Xe (14.1 L - 79.3 g) will used at the next step of the experiment to increase a sensitivity of 2 K -caption of 124 Xe registration. In this case sensitivity to the investigated process will be at the level of S = 1.46 × 10 21 yr (90% C.L.) for 1 year measurement.