Index: Lib/posixpath.py
===================================================================
--- Lib/posixpath.py	(revision 77442)
+++ Lib/posixpath.py	(working copy)
@@ -337,7 +337,11 @@
 def abspath(path):
     """Return an absolute path."""
     if not isabs(path):
-        path = join(os.getcwd(), path)
+        if isinstance(path, unicode):
+            cwd = os.getcwdu()
+        else:
+            cwd = os.getcwd()
+        path = join(cwd, path)
     return normpath(path)
 
 
Index: Lib/test/test_support.py
===================================================================
--- Lib/test/test_support.py	(revision 77441)
+++ Lib/test/test_support.py	(working copy)
@@ -612,6 +612,22 @@
         sys.path[:] = self.original_value
 
 
+class TempCWD(object):
+    def __init__(self, dirname='tempdir'):
+        self.dirname = os.path.join(TESTFN, dirname)
+        self._oldcwd = os.getcwd()
+
+    def __enter__(self):
+        if not os.path.exists(self.dirname):
+            os.makedirs(self.dirname)
+        os.chdir(self.dirname)
+        return self.dirname
+
+    def __exit__(self, exc, value, tb):
+        os.chdir(self._oldcwd)
+        rmtree(os.path.dirname(self.dirname))
+
+
 class TransientResource(object):
 
     """Raise ResourceDenied if an exception is raised while the context manager
Index: Lib/test/test_posixpath.py
===================================================================
--- Lib/test/test_posixpath.py	(revision 77442)
+++ Lib/test/test_posixpath.py	(working copy)
@@ -28,6 +28,12 @@
     def assertIs(self, a, b):
         self.assertTrue(a is b)
 
+    def assertStr(self, s):
+        self.assertTrue(isinstance(s, str), '%r is not str' % s)
+
+    def assertUnicode(self, s):
+        self.assertTrue(isinstance(s, unicode), '%r is not unicode' % s)
+
     def test_normcase(self):
         # Check that normcase() is idempotent
         p = "FoO/./BaR"
@@ -391,6 +397,23 @@
     def test_abspath(self):
         self.assertTrue("foo" in posixpath.abspath("foo"))
 
+        # Issue 3426: check that abspath retuns unicode when the arg is unicode
+        # and str when it's str, with both ASCII/non-ASCII str/unicode cwds
+
+        # test non absolute paths, os.getcwd/getcwdu are called
+        for path in ('cwd', '\xe7w\xf0'):
+            with test_support.TempCWD(path):
+                self.assertStr(posixpath.abspath("foo"))
+                self.assertStr(posixpath.abspath("f\xf2\xf2"))
+        for upath in (u'cwdu', u'\xe7w\xf0u'):
+            with test_support.TempCWD(upath):
+                self.assertUnicode(posixpath.abspath(u"fuu"))
+                self.assertUnicode(posixpath.abspath(u"f\xf9\xf9"))
+
+        # test absolute paths, os.getcwd/getcwdu are not called
+        self.assertStr(posixpath.abspath("/foo"))
+        self.assertUnicode(posixpath.abspath(u"/foo"))
+
         self.assertRaises(TypeError, posixpath.abspath)
 
     def test_realpath(self):