No, that is forbidden by statute:
KRS 402.010. Degree of relationship that will bar marriage.
(1) No marriage shall be contracted between persons who are nearer of kin to each other by consanguinity, whether of the whole or half-blood, than second cousins.
(2) Marriages prohibited by subsection (1) of this section are incestuous and void.
Further, a marriage between first cousins will not be recognized in Kentucky even if it is consummated in another state.
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