  Given a tropical variety X and two non-negative integers p and q we define
homology group $H_{p,q}(X)$. We show that if X is a smooth tropical variety
that can be represented as the tropical limit of a 1-parameter family of
complex projective varieties, then $\dim H_{p,q}(X)$ coincides with the Hodge
number $h^{p,q}$ of a general member of the family.
