Can a government employee hold the chief position in an ngo?

He can, if the position is voluntary & without any payment.

He should obtain permission from his department being a government employee to indulge in such extra curricular activities which may  prove a hindrance/disturbance to his service career.

Under the Government Servant's Conduct Rules applicable to Central Government Servants, no permission is necessary, if the NGO is registered under the Societies' Registration Act. I do not remember the Rule No. You may be able to find out from the internet.  But just to avoid any harassment let your brother inform his department and wait for some time. If no reply is received he can go ahead. If a 'no' reply is received, it cannot be arbitrary. The Government has to give valid reason.

The Central Government Rule says that there is no bar for Governments servants to join purely artistic, literary, scientific or charitable organizations,which are not a source of profit. But if your brother's superior officer asks him not to be associated, he will have to refrain from. It will be an uphill task to get clearance again. But if the order of the superior officer does not come within reasonable time no action can be taken against your brother.

I have checked the Rules of a few State Governments. They are also a repetition of same Rule only.

permission of deptt is very well requuired by govt servant. 

Can the trust (ngo) members instal their display board of designation on their vehicle?