Make posix.putenv() raise ValueError if name is empty.

diff --git a/Doc/library/os.rst b/Doc/library/os.rst
--- a/Doc/library/os.rst
+++ b/Doc/library/os.rst
@@ -253,8 +253,8 @@ process and user.
 
    Set the environment variable named *varname* to the string *value*.  Such
    changes to the environment affect subprocesses started with :func:`os.system`,
-   :func:`popen` or :func:`fork` and :func:`execv`.  Raises :exc:`ValueError`
-   if *varname* contains an ``'='`` character.
+   :func:`popen` or :func:`fork` and :func:`execv`.  May raise
+   :exc:`ValueError` if *varname* is empty or contains an ``'='`` character.
 
    Availability: most flavors of Unix, Windows.
 
diff --git a/Lib/test/test_os.py b/Lib/test/test_os.py
--- a/Lib/test/test_os.py
+++ b/Lib/test/test_os.py
@@ -352,6 +352,8 @@ class EnvironTests(mapping_tests.BasicTe
                           "PYTHONTESTVAROS=SOMETHING", "value")
         self.assertTrue("PYTHONTESTVAROS=SOMETHING" not in os.environ)
         self.assertTrue("PYTHONTESTVAROS" not in os.environ)
+        self.assertRaises(ValueError, os.environ.__setitem__, "", "value")
+        self.assertTrue("" not in os.environ)
 
 class WalkTests(unittest.TestCase):
     """Tests for os.walk()."""
diff --git a/Lib/test/test_posix.py b/Lib/test/test_posix.py
--- a/Lib/test/test_posix.py
+++ b/Lib/test/test_posix.py
@@ -340,6 +340,7 @@ class PosixTester(unittest.TestCase):
         # See issue #4926
         self.assertRaises(ValueError, posix.putenv,
                           "PYTHONTESTVARB=SOMETHING", "value")
+        self.assertRaises(ValueError, posix.putenv, "", "value")
 
     def test_getcwd_long_pathnames(self):
         if hasattr(posix, 'getcwd'):
diff --git a/Modules/posixmodule.c b/Modules/posixmodule.c
--- a/Modules/posixmodule.c
+++ b/Modules/posixmodule.c
@@ -6868,6 +6868,21 @@ posix_putenv(PyObject *self, PyObject *a
     if (!PyArg_ParseTuple(args, "ss:putenv", &s1, &s2))
         return NULL;
 
+    /* XXX: logically, there is no problem with an environment
+       variable having an empty name, but POSIX requires unsetenv() to
+       refuse to delete such a variable, which can be a problem (on
+       Linux, for instance, such a variable can be passed to a new
+       process, but cannot be deleted with unsetenv()).  The return
+       value of unsetenv() is currently not checked (some systems
+       declare it as void), so an object added to posix_putenv_garbage
+       for an empty-named variable could be freed while the
+       environment still pointed into it. */
+    if (*s1 == 0) {
+        PyErr_SetString(PyExc_ValueError, "environment variable name must "
+                        "not be empty");
+        return NULL;
+    }
+
     /* An '=' character would be interpreted as the end of the name. */
     if (strchr(s1, '=') != NULL) {
         PyErr_SetString(PyExc_ValueError, "environment variable name must "