Source : Webster's Revised Unabridged Dictionary (1913)

Legitimately \Le*git"i*mate*ly\ (-m[asl]t*l[y^]), adv.
   In a legitimate manner; lawfully; genuinely.

Source : WordNet®

legitimately
     adv 1: in a manner acceptable to common custom; "you cannot do this
            legitimately!" [syn: {lawfully}, {licitly}] [ant: {illegitimately},
             {illegally}, {illegitimately}]
     2: in a lawfully recognized manner; "let's get married so our
        child can be born legitimately" [ant: {illegitimately}]