diff --git a/mypy/myunit/__main__.py b/mypy/myunit/__main__.py
index 34098d40648d..78ef01f6012f 100644
--- a/mypy/myunit/__main__.py
+++ b/mypy/myunit/__main__.py
@@ -6,4 +6,13 @@
 
 from mypy.myunit import main
 
+# In Python 3.3, mypy.__path__ contains a relative path to the mypy module
+# (whereas in later Python versions it contains an absolute path).  Because the
+# test runner changes directories, this breaks non-toplevel mypy imports.  We
+# fix that problem by fixing up the path to be absolute here.
+import os.path
+import mypy
+# User-defined packages always have __path__ attributes, but mypy doesn't know that.
+mypy.__path__ = [os.path.abspath(p) for p in mypy.__path__]  # type: ignore
+
 main()
diff --git a/mypy/test/data/check-fastparse.test b/mypy/test/data/check-fastparse.test
new file mode 100644
index 000000000000..192fa5ee482e
--- /dev/null
+++ b/mypy/test/data/check-fastparse.test
@@ -0,0 +1,25 @@
+[case testFastParseSyntaxError]
+# flags: fast-parser
+1 +  # E: invalid syntax
+
+[case testFastParseTypeCommentSyntaxError]
+# flags: fast-parser
+x = None # type: a : b  # E: syntax error in type comment
+
+[case testFastParseInvalidTypeComment]
+# flags: fast-parser
+x = None # type: a + b  # E: invalid type comment
+
+-- Function type comments are attributed to the function def line.
+-- This happens in both parsers.
+[case testFastParseFunctionAnnotationSyntaxError]
+# flags: fast-parser
+def f():  # E: syntax error in type comment
+  # type: None -> None
+  pass
+
+[case testFastParseInvalidFunctionAnnotation]
+# flags: fast-parser
+def f():  # E: invalid type comment
+  # type: (a + b) -> None
+  pass
diff --git a/mypy/test/testcheck.py b/mypy/test/testcheck.py
index 412693a39acb..b7975e3a8cc4 100644
--- a/mypy/test/testcheck.py
+++ b/mypy/test/testcheck.py
@@ -57,6 +57,7 @@
     'check-flags.test',
     'check-incremental.test',
     'check-bound.test',
+    'check-fastparse.test',
 ]
 
 
diff --git a/runtests.py b/runtests.py
index c82fd0b92e83..82b42c3f58a4 100755
--- a/runtests.py
+++ b/runtests.py
@@ -155,7 +155,7 @@ def add_basic(driver: Driver) -> None:
     driver.add_mypy('legacy myunit script', 'scripts/myunit')
     driver.add_flake8('legacy myunit script', 'scripts/myunit')
     # needs typed_ast installed:
-    # driver.add_mypy('fast-parse', '--fast-parse', 'samples/hello.py')
+    driver.add_mypy('fast-parse', '--fast-parse', 'samples/hello.py')
 
 
 def add_selftypecheck(driver: Driver) -> None:
@@ -184,10 +184,7 @@ def add_imports(driver: Driver) -> None:
         mod = file_to_module(f)
         if '.test.data.' in mod:
             continue
-        # Don't check the importability of the fastparse module because it
-        # requires typed_ast which may not be available (but which we don't
-        # want to have an explicit dependency on yet)
-        if not mod.endswith('.__main__') and not mod.endswith('.fastparse'):
+        if not mod.endswith('.__main__'):
             driver.add_python_string('import %s' % mod, 'import %s' % mod)
         driver.add_flake8('module %s' % mod, f)
 
diff --git a/test-requirements.txt b/test-requirements.txt
index 39304807fbc7..47744fe21aac 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1 +1,2 @@
 flake8
+typed-ast