Can we have a linux terminal chat client for gmail?

Does a gmail terminal chat client exist or anyway one can write it?

Yes. Gmail uses the Jabber chat protocol which has been around for much longer than gchat and is supported by a number of open source command line chatting programs. One of my favorite terminal chat clients is Centericq which supports jabber along with many other chat protocol. It is ncurses based:

To connect to gchat use these settings:

Username: Your Google Talk username (without any @ symbol or domain information)
Password: Your password
Login Server: Enter the portion of your email address after the @ symbol. For example, [email protected] will enter example.com as the Login Server value.
Use SSL: Yes
Manually specify connection host: Yes
Host: talk.google.com
Port: 5223
Keep connection alive: Yes

Part of the Pidgin IM client is a terminal based client called Finch. Take a look at the Using Finch page on the Pidgin wiki.

Bitlbee provides an IRC interface to most of the common chat protocols. Mix with Irssi or your CLI IRC client of choice.

MCabber should also work just fine. It supports OTR also (which is crucial if we talk about Google and nowadays internet).

(MCabber is my favorite by the way. I tried all the alternatives but this seemed to be the best so far. It just works, it's just excellent.)