diff --git a/tornado/test/template_test.py b/tornado/test/template_test.py
index 41c1c90c..c19728e1 100644
--- a/tornado/test/template_test.py
+++ b/tornado/test/template_test.py
@@ -6,8 +6,8 @@ import traceback
 
 from tornado.escape import utf8, native_str, to_unicode
 from tornado.template import Template, DictLoader, ParseError, Loader
-from tornado.test.util import unittest, is_coverage_running
-from tornado.util import ObjectDict, unicode_type, PY3
+from tornado.test.util import unittest
+from tornado.util import ObjectDict, unicode_type
 
 
 class TemplateTest(unittest.TestCase):
@@ -175,11 +175,6 @@ try{% set y = 1/x %}
         self.assertEqual(template.generate(), '0')
 
     def test_non_ascii_name(self):
-        if PY3 and is_coverage_running():
-            try:
-                os.fsencode(u"t\u00e9st.html")
-            except UnicodeEncodeError:
-                self.skipTest("coverage tries to access unencodable filename")
         loader = DictLoader({u"t\u00e9st.html": "hello"})
         self.assertEqual(loader.load(u"t\u00e9st.html").generate(), b"hello")
 
diff --git a/tornado/test/util.py b/tornado/test/util.py
index 1d998f0e..63a9762f 100644
--- a/tornado/test/util.py
+++ b/tornado/test/util.py
@@ -97,24 +97,6 @@ def exec_test(caller_globals, caller_locals, s):
     return local_namespace
 
 
-def is_coverage_running():
-    """Return whether coverage is currently running.
-    """
-    if 'coverage' not in sys.modules:
-        return False
-    tracer = sys.gettrace()
-    if tracer is None:
-        return False
-    try:
-        mod = tracer.__module__
-    except AttributeError:
-        try:
-            mod = tracer.__class__.__module__
-        except AttributeError:
-            return False
-    return mod.startswith('coverage')
-
-
 def subTest(test, *args, **kwargs):
     """Compatibility shim for unittest.TestCase.subTest.