diff --git a/Tests/images/hopper_palette_chunk_second.fli b/Tests/images/hopper_palette_chunk_second.fli
new file mode 100644
index 00000000000..54447de0af7
Binary files /dev/null and b/Tests/images/hopper_palette_chunk_second.fli differ
diff --git a/Tests/test_file_fli.py b/Tests/test_file_fli.py
index a7d43d2e922..b8b999d70d0 100644
--- a/Tests/test_file_fli.py
+++ b/Tests/test_file_fli.py
@@ -4,7 +4,7 @@
 
 from PIL import FliImagePlugin, Image
 
-from .helper import assert_image_equal_tofile, is_pypy
+from .helper import assert_image_equal, assert_image_equal_tofile, is_pypy
 
 # created as an export of a palette image from Gimp2.6
 # save as...-> hopper.fli, default options.
@@ -79,6 +79,12 @@ def test_invalid_file():
         FliImagePlugin.FliImageFile(invalid_file)
 
 
+def test_palette_chunk_second():
+    with Image.open("Tests/images/hopper_palette_chunk_second.fli") as im:
+        with Image.open(static_test_file) as expected:
+            assert_image_equal(im.convert("RGB"), expected.convert("RGB"))
+
+
 def test_n_frames():
     with Image.open(static_test_file) as im:
         assert im.n_frames == 1
diff --git a/src/PIL/FliImagePlugin.py b/src/PIL/FliImagePlugin.py
index e13b1779ccc..908bed9f427 100644
--- a/src/PIL/FliImagePlugin.py
+++ b/src/PIL/FliImagePlugin.py
@@ -15,6 +15,7 @@
 # See the README file for information on usage and redistribution.
 #
 
+import os
 
 from . import Image, ImageFile, ImagePalette
 from ._binary import i16le as i16
@@ -80,11 +81,19 @@ def _open(self):
 
         if i16(s, 4) == 0xF1FA:
             # look for palette chunk
-            s = self.fp.read(6)
-            if i16(s, 4) == 11:
-                self._palette(palette, 2)
-            elif i16(s, 4) == 4:
-                self._palette(palette, 0)
+            number_of_subchunks = i16(s, 6)
+            chunk_size = None
+            for _ in range(number_of_subchunks):
+                if chunk_size is not None:
+                    self.fp.seek(chunk_size - 6, os.SEEK_CUR)
+                s = self.fp.read(6)
+                chunk_type = i16(s, 4)
+                if chunk_type in (4, 11):
+                    self._palette(palette, 2 if chunk_type == 11 else 0)
+                    break
+                chunk_size = i32(s)
+                if not chunk_size:
+                    break
 
         palette = [o8(r) + o8(g) + o8(b) for (r, g, b) in palette]
         self.palette = ImagePalette.raw("RGB", b"".join(palette))