Another method for those who really want to do this in spite of the correct remarks that you shouldn't:
import unittest
class MyTest(unittest.TestCase):
def __init__(self, testName, extraArg):
super(MyTest, self).__init__(testName) # calling the super class init varies for different python versions. This works for 2.7
self.myExtraArg = extraArg
def test_something(self):
print(self.myExtraArg)
# call your test
suite = unittest.TestSuite()
suite.addTest(MyTest('test_something', extraArg))
unittest.TextTestRunner(verbosity=2).run(suite)