  A technique to search for 2K-capture of $^{78}$Kr with large low-background
proportional counter filled with an enriched in $^{78}$Kr up to 99.8% sample of
Krypton at a pressure of 4.51 is described in this paper. The results of first
measurements are presented. Analysis of data collected during 159 hours yielded
new limit to the half-life of $^{78}$Kr with regard to 2K-capture
(T$_{1/2}\geq6\cdot10^{21}$ yr (90% C.L.)). Sensitivity of the facility to the
process for one year of measurement was evaluated to be
$\texttt{S}=1.0\cdot10^{22}$ yr (90% C.L.).
