In this paper, we study a specific hidden Markov chain defined by the equation: $Y_i=X_i+\varepsilon_i$, $i=1,\ldots,n+1$, where $(X_i)_{i \geq 1}$ is a real-valued stationary Markov chain and $(\varepsilon_i)_{i \geq 1}$ is a noise independent of $(X_i)_{i\geq 1}$. We develop a new parametric approach obtained by minimization of a particular contrast taking advantage of the regressive problem and based on deconvolution strategy. We provide theoretical guarantees on the performance of the resulting estimator; its consistency and its asymptotic normality are established.