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
@@ -331,8 +331,8 @@ process and user.
 
    Set the environment variable named *key* 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 *key* contains an ``'='`` character.
+   :func:`popen` or :func:`fork` and :func:`execv`.  May raise
+   :exc:`ValueError` if *key* 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
@@ -405,6 +405,8 @@ 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)
 
     def test_os_popen_iter(self):
         if os.path.exists("/bin/sh"):
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
@@ -327,6 +327,7 @@ 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
@@ -5803,6 +5803,21 @@ posix_putenv(PyObject *self, PyObject *a
     s2 = PyBytes_AsString(os2);
 #endif
 
+    /* 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");
+        goto error;
+    }
+
     /* An '=' character would be interpreted as the end of the name. */
 #ifdef MS_WINDOWS
     if (wcschr(s1, L'=') != NULL) {