Can some body chat with Christian girl to invite her to Islam on the Internet?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

A man can call a woman to Islam through the Internet but not using "chat". This should be done through reminding her of Allah and of His Punishment and Reward. One should remind her of the Doomsday and that she will stand in front of Allah without any mediator. Also, one should tell her about the greatness of Islam and that it is the only true religion and so on.
As for the "chat", it has more disadvantages than advantages.

It should be mentioned here that Satan's whispers can influence the way a man calls a woman to become Muslim.

So, pious women would be much better and more appropriate to carry out this mission.

Allah knows best.