python3 is my local Anaconda version of python, while python3.4 is the system one. I can import gi module with python3.4
python3
python3.4
gi
If you're using conda virtualenv for python-3, you can use
$ conda install -c conda-forge pygobject
in your virtualenv
You can read more about this on: https://anaconda.org/conda-forge/pygobject