diff --git a/Lib/fontTools/feaLib/parser.py b/Lib/fontTools/feaLib/parser.py
index 631165dfe..7902773f2 100644
--- a/Lib/fontTools/feaLib/parser.py
+++ b/Lib/fontTools/feaLib/parser.py
@@ -17,7 +17,19 @@ class Parser(object):
     extensions = {}
     ast = ast
 
-    def __init__(self, featurefile, glyphNames):
+    def __init__(self, featurefile, glyphNames=(), **kwargs):
+        if "glyphMap" in kwargs:
+            from fontTools.misc.loggingTools import deprecateArgument
+            deprecateArgument("glyphMap", "use 'glyphNames' (iterable) instead")
+            if glyphNames:
+                raise TypeError("'glyphNames' and (deprecated) 'glyphMap' are "
+                                "mutually exclusive")
+            glyphNames = kwargs.pop("glyphMap")
+        if kwargs:
+            raise TypeError("unsupported keyword argument%s: %s"
+                            % ("" if len(kwargs) == 1 else "s",
+                               ", ".join(repr(k) for k in kwargs)))
+
         self.glyphNames_ = set(glyphNames)
         self.doc_ = self.ast.FeatureFile()
         self.anchors_ = SymbolTable()
diff --git a/Tests/feaLib/parser_test.py b/Tests/feaLib/parser_test.py
index fd053a776..b9606406c 100644
--- a/Tests/feaLib/parser_test.py
+++ b/Tests/feaLib/parser_test.py
@@ -4,6 +4,7 @@ from __future__ import unicode_literals
 from fontTools.feaLib.error import FeatureLibError
 from fontTools.feaLib.parser import Parser, SymbolTable
 from fontTools.misc.py23 import *
+import warnings
 import fontTools.feaLib.ast as ast
 import os
 import unittest
@@ -51,6 +52,25 @@ class ParserTest(unittest.TestCase):
         if not hasattr(self, "assertRaisesRegex"):
             self.assertRaisesRegex = self.assertRaisesRegexp
 
+    def test_glyphMap_deprecated(self):
+        glyphMap = {'a': 0, 'b': 1, 'c': 2}
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter("always")
+            parser = Parser(UnicodeIO(), glyphMap=glyphMap)
+
+            self.assertEqual(len(w), 1)
+            self.assertEqual(w[-1].category, UserWarning)
+            self.assertIn("deprecated", str(w[-1].message))
+            self.assertEqual(parser.glyphNames_, {'a', 'b', 'c'})
+
+            self.assertRaisesRegex(
+                TypeError, "mutually exclusive",
+                Parser, UnicodeIO(), ("a",), glyphMap={"a": 0})
+
+            self.assertRaisesRegex(
+                TypeError, "unsupported keyword argument",
+                Parser, UnicodeIO(), foo="bar")
+
     def test_comments(self):
         doc = self.parse(
             """ # Initial