Can a muslim girl marry a christian boy?

Yes she can marry the boy ONLY AFTER he accepts Islam willingly and convinced of its truth. There should be no conversion for marriage sake. Also be it boy or girl they shouldn't have any personal communication with na mehram which can lead to such fitnah (temptation) of falling in love traps etc... Hijab prescribed for both men and women include hijab of eyes (what we see), hijab of tongue (what we speak), hijab of hands, hijab of legs, hijab of heart.
Hope it helps