Python3 cannot import gi

python packages installed system-wide may not be available for python versions installed in anaconda directories.

Try instead to load your script using the full path to the system interpreter:

$ /usr/bin/python3
Python 3.4.0 (default, Apr 11 2014, 13:05:11) 
[GCC 4.8.2] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import gi
>>> 

Some packages like gi does not exist in the conda environment directory after installation but the system's Python directory. You could use conda-forge to install the package so that could run it directly from your conda Python 3 environment.

conda install -c conda-forge pygobject