What happened to ChmSee in 14.04?

Because it is not mantained anymore.
From its official webpage:

News
2013-08-25: Stop maintain.

I think that if you want to go in and developing/mantaining it no one will stop you! :D

Why ChmSee was removed from 14.04 Trusty-Tahr?

As first answered by dadexix86, it's because ChmSee is not maintained anymore by the upstream.

How to install and use ChmSee on 14.04 the nice way?

Several other people have tried to answer this using PPA and adding new repositories. But these are not methods I consider nice! Feel free to disagree with me but this is how I personally feel fit.

The method of my preference is as follows:

1. Go to the Ubuntu-packages page on chmsee for Saucy.
2. At the botton of the page, download the proper .deb package for your system.

3. The list of dependencies for this package is also listed in that page. Install them using the following command (though, all of them were already installed on my system):

   sudo apt-get install libc6 libchm1 libgcrypt11 libgdk-pixbuf2.0-0 libglib2.0-0 libgtk2.0-0 libpango1.0-0 libwebkitgtk-1.0-0 libxml2

4. Install the package:

   for 32-bit systems:

   sudo dpkg -i chmsee_1.3.0-2ubuntu2_i386.deb
   

   for 64-bit systems:

   sudo dpkg -i chmsee_1.3.0-2ubuntu2_amd64.deb
   

I have tested this on my own 14.04 machine and I can confirm it works.

After trying, here is a little summary of alternative chm reader:

xchm

Designed for xice, but also good for gnome/kde. This seems to be the simplest & best choice for ubuntu 14.04+.

install: sudo apt-get install xchm

kchmviewer

Design for kde, but also could use on gnome.

install: sudo apt-get install kchmviewer

Tip: on gnome, the installation need install kde related package (e.g kde-runtime), thus need download a lot (around 60Mb), and take a lot disk space (around 140Mb).

You can download ChmSee Run the following code:

wget -q -O - http://archive.getdeb.net/getdeb-archive.key | sudo apt-key add -
sudo sh -c 'echo "deb http://archive.getdeb.net/ubuntu trusty-getdeb apps" >> /etc/apt/sources.list.d/getdeb.list'

and then install it using:

sudo apt-get install chmsee