diff --git a/changelog/new_layout_spacearoundsingletonclassoperator.md b/changelog/new_layout_spacearoundsingletonclassoperator.md
new file mode 100644
index 00000000000..742534ab757
--- /dev/null
+++ b/changelog/new_layout_spacearoundsingletonclassoperator.md
@@ -0,0 +1 @@
+* [#8469](https://github.com/rubocop/rubocop/issues/8469): Add cop `Layout/SpaceAroundSingletonClassOperator`. ([@jonas054][])
diff --git a/config/default.yml b/config/default.yml
index 11af268c520..147efbe700a 100644
--- a/config/default.yml
+++ b/config/default.yml
@@ -1226,6 +1226,15 @@ Layout/SpaceAroundOperators:
     - space
     - no_space
 
+Layout/SpaceAroundSingletonClassOperator:
+  Description: 'Use a single space around the singleton class operator.'
+  Enabled: pending
+  VersionAdded: '<<next>>'
+  EnforcedStyle: space
+  SupportedStyles:
+    - space
+    - no_space
+
 Layout/SpaceBeforeBlockBraces:
   Description: >-
                  Checks that the left block brace has or doesn't have space
diff --git a/lib/rubocop.rb b/lib/rubocop.rb
index c9a937ea142..cfdb5222761 100644
--- a/lib/rubocop.rb
+++ b/lib/rubocop.rb
@@ -238,6 +238,7 @@
 require_relative 'rubocop/cop/layout/space_around_keyword'
 require_relative 'rubocop/cop/layout/space_around_method_call_operator'
 require_relative 'rubocop/cop/layout/space_around_operators'
+require_relative 'rubocop/cop/layout/space_around_singleton_class_operator'
 require_relative 'rubocop/cop/layout/space_before_block_braces'
 require_relative 'rubocop/cop/layout/space_before_brackets'
 require_relative 'rubocop/cop/layout/space_before_comma'
diff --git a/lib/rubocop/cop/layout/space_around_singleton_class_operator.rb b/lib/rubocop/cop/layout/space_around_singleton_class_operator.rb
new file mode 100644
index 00000000000..f9966ececd7
--- /dev/null
+++ b/lib/rubocop/cop/layout/space_around_singleton_class_operator.rb
@@ -0,0 +1,53 @@
+# frozen_string_literal: true
+
+module RuboCop
+  module Cop
+    module Layout
+      # Checks if spaces are used around the singleton class operator <<.
+      #
+      # @example EnforcedStyle: space (default)
+      #   # bad
+      #   class SomeClass
+      #     class<<self
+      #     end
+      #   end
+      #
+      #   # good
+      #   class SomeClass
+      #     class << self
+      #     end
+      #   end
+      #
+      # @example EnforcedStyle: no_space
+      #   # bad
+      #   class SomeClass
+      #     class << self
+      #     end
+      #   end
+      #
+      #   # good
+      #   class SomeClass
+      #     class<<self
+      #     end
+      #   end
+      #
+      class SpaceAroundSingletonClassOperator < Base
+        include RangeHelp
+        include ConfigurableEnforcedStyle
+
+        MSG_SPACE = 'Use a single space around the singleton class operator.'
+        MSG_NO_SPACE = 'Use no space around the singleton class operator.'
+
+        def on_sclass(node)
+          range = range_with_surrounding_space(range: node.loc.operator)
+          case style
+          when :space
+            add_offense(range, message: MSG_SPACE) if range.source != ' << '
+          else
+            add_offense(range, message: MSG_NO_SPACE) if range.source != '<<'
+          end
+        end
+      end
+    end
+  end
+end
diff --git a/spec/rubocop/cop/layout/space_around_singleton_class_operator_spec.rb b/spec/rubocop/cop/layout/space_around_singleton_class_operator_spec.rb
new file mode 100644
index 00000000000..b253f844230
--- /dev/null
+++ b/spec/rubocop/cop/layout/space_around_singleton_class_operator_spec.rb
@@ -0,0 +1,65 @@
+# frozen_string_literal: true
+
+RSpec.describe RuboCop::Cop::Layout::SpaceAroundSingletonClassOperator, :config do
+  context 'when EnforcedStyle is space' do
+    let(:cop_config) { { 'EnforcedStyle' => 'space' } }
+
+    it 'registers an offense for no space to the left`' do
+      expect_offense(<<~RUBY)
+        class<< self
+             ^^^ Use a single space around the singleton class operator.
+        end
+      RUBY
+    end
+
+    it 'registers an offense for no space to the right`' do
+      expect_offense(<<~RUBY)
+        class <<Other
+             ^^^ Use a single space around the singleton class operator.
+        end
+      RUBY
+    end
+
+    it 'registers an offense for no space at all`' do
+      expect_offense(<<~RUBY)
+        class<<self
+             ^^ Use a single space around the singleton class operator.
+        end
+      RUBY
+    end
+
+    it 'does not register an offense for << surrounded by single spaces' do
+      expect_no_offenses(<<~RUBY)
+        class << self
+        end
+      RUBY
+    end
+  end
+
+  context 'when EnforcedStyle is no_space' do
+    let(:cop_config) { { 'EnforcedStyle' => 'no_space' } }
+
+    it 'registers an offense for space to the left`' do
+      expect_offense(<<~RUBY)
+        class <<self
+             ^^^ Use no space around the singleton class operator.
+        end
+      RUBY
+    end
+
+    it 'registers an offense for space to the right`' do
+      expect_offense(<<~RUBY)
+        class<< self
+             ^^^ Use no space around the singleton class operator.
+        end
+      RUBY
+    end
+
+    it 'does not register an offense for << surrounded by no space' do
+      expect_no_offenses(<<~RUBY)
+        class<<self
+        end
+      RUBY
+    end
+  end
+end