diff --git a/.travis.yml b/.travis.yml
index 89102f4a..e3b32895 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -32,6 +32,7 @@ matrix:
       script:
         # Ignore F401, which are unused imports. flake8 is a primitive tool and is sometimes wrong.
         - 'flake8 --extend-ignore F401 jedi setup.py'
+        - 'mypy jedi'
 install:
     - sudo apt-get -y install python3-venv
     - pip install .[testing]
diff --git a/setup.cfg b/setup.cfg
index 6929ce30..54fd65db 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -19,3 +19,35 @@ exclude = jedi/third_party/* .tox/*
 
 [pycodestyle]
 max-line-length = 100
+
+
+[mypy]
+# Ensure generics are explicit about what they are (e.g: `List[str]` rather than
+# just `List`)
+disallow_any_generics = True
+
+disallow_subclassing_any = True
+
+# Ensure that optional types are explicit
+no_implicit_optional = True
+strict_optional = True
+
+# Avoid creating future gotchas emerging from bad typing
+warn_redundant_casts = True
+warn_unused_ignores = True
+warn_return_any = True
+warn_unused_configs = True
+
+warn_unreachable = True
+
+# Require values to be explicitly re-exported; this makes things easier for
+# Flake8 too and avoids accidentally importing thing from the "wrong" place
+# (which helps avoid circular imports)
+implicit_reexport = False
+
+strict_equality = True
+
+[mypy-jedi.debug]
+# jedi.debug is configured by setting module-level values, which mypy doesn't
+# know about.
+warn_unreachable = False
diff --git a/setup.py b/setup.py
index bf9be8c2..b4f9da2a 100755
--- a/setup.py
+++ b/setup.py
@@ -46,6 +46,7 @@ setup(name='jedi',
           ],
           'qa': [
               'flake8==3.8.3',
+              'mypy==0.782',
           ],
       },
       package_data={'jedi': ['*.pyi', 'third_party/typeshed/LICENSE',