2018 Update: This is still attracting upvotes which worries me.

12.04 has been unsupported for about a year now. The best way you can install pip3 is by upgrading to a newer, supported version of Ubuntu. You have 3 LTS versions to pick from.

While on more modern versions of Ubuntu you could just sudo apt-get install python3-pip (and then use pip3), a Python 3 copy of pip was never packaged for 12.04.

Therefore you need to follow the more old fashioned install route with easy_install:

sudo apt-get install python3-setuptools

sudo easy_install3 pip

Now, there is every chance that this will clash with Python 2's pip and override /usr/bin/pip, because it will install a python3 based /usr/local/bin/pip which is also in Ubuntu 12.04's $PATH.

It shouldn't overwrite it so as long as you know that, it might be acceptable. However it might be best to start investigating the happy world of virtualenv as this answer suggests.

Alternatively you could rename the easy-installed python3 version of pip:

sudo mv /usr/local/bin/pip /usr/local/bin/pip-3

Then you can confirm your existing pip is still python2.7 based:

pip --version