We report the specific heat (SH) measurements on single crystals of hole doped $FeAs$-based superconductor $Ba_{0.6}K_{0.4}Fe_2As_2$. It is found that the electronic SH coefficient $gamma_e(T)$ is not temperature dependent and increases almost linearly with the magnetic field in low temperature region. These point to a fully gapped superconducting state. Surprisingly the sharp SH anomaly $Delta C/T|_{T_c}$ reaches a value of 98 $mJ/mol K^2$ suggesting a very high normal state quasiparticle density of states ($gamma_n approx 63 mJ/mol K^2$). A detailed analysis reveals that the $gamma_e(T)$ cannot be fitted with a single gap of s-wave symmetry due to the presence of a hump in the middle temperature region. However, our data indicate that the dominant part of the superconducting condensate is induced by an s-wave gap with the magnitude of about 6 meV.
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