diff --git a/pkg/chezmoi/sourcestate.go b/pkg/chezmoi/sourcestate.go
index 4e8f1969c46..bdb2d713a1c 100644
--- a/pkg/chezmoi/sourcestate.go
+++ b/pkg/chezmoi/sourcestate.go
@@ -2157,6 +2157,7 @@ func (s *SourceState) readExternalDir(
 				TargetName: fileInfo.Name(),
 				Type:       SourceFileTypeFile,
 				Empty:      true,
+				Executable: isExecutable(fileInfo),
 				Private:    isPrivate(fileInfo),
 				ReadOnly:   isReadOnly(fileInfo),
 			}
diff --git a/pkg/cmd/testdata/scripts/issue2964.txtar b/pkg/cmd/testdata/scripts/issue2964.txtar
new file mode 100644
index 00000000000..2eacf91f6cb
--- /dev/null
+++ b/pkg/cmd/testdata/scripts/issue2964.txtar
@@ -0,0 +1,11 @@
+[windows] skip 'UNIX only'
+
+chmod 755 $CHEZMOISOURCEDIR/external_dot_dir/executable
+
+# test that external_ directories respect the executable bit
+exec chezmoi apply
+[umask:002] cmpmod 775 $HOME/.dir/executable
+[umask:022] cmpmod 755 $HOME/.dir/executable
+
+-- home/user/.local/share/chezmoi/external_dot_dir/executable --
+# contents of .dir/executable