diff --git a/changelog/fix_space_around_singleton_class_operator.md b/changelog/fix_space_around_singleton_class_operator.md
new file mode 100644
index 00000000000..a07d33720e3
--- /dev/null
+++ b/changelog/fix_space_around_singleton_class_operator.md
@@ -0,0 +1 @@
+* [#8469](https://github.com/rubocop/rubocop/issues/8469): Add inspection of `class <<` to `Layout/SpaceAroundOperators`. ([@jonas054][])
diff --git a/lib/rubocop/cop/layout/space_around_operators.rb b/lib/rubocop/cop/layout/space_around_operators.rb
index 3e72bb23bfa..e03d57b9116 100644
--- a/lib/rubocop/cop/layout/space_around_operators.rb
+++ b/lib/rubocop/cop/layout/space_around_operators.rb
@@ -63,6 +63,10 @@ def self.autocorrect_incompatible_with
           [Style::SelfAssignment]
         end
 
+        def on_sclass(node)
+          check_operator(:sclass, node.loc.operator, node.source_range)
+        end
+
         def on_pair(node)
           return unless node.hash_rocket?
 
diff --git a/spec/rubocop/cop/layout/space_around_operators_spec.rb b/spec/rubocop/cop/layout/space_around_operators_spec.rb
index 8cbe15701fe..a2fa14295d1 100644
--- a/spec/rubocop/cop/layout/space_around_operators_spec.rb
+++ b/spec/rubocop/cop/layout/space_around_operators_spec.rb
@@ -278,9 +278,15 @@ def init(name=nil)
     RUBY
   end
 
-  it 'accepts the construct class <<self with no space after <<' do
-    expect_no_offenses(<<~RUBY)
-      class <<self
+  it 'registers an offense and corrects singleton class operator`' do
+    expect_offense(<<~RUBY)
+      class<<self
+           ^^ Surrounding space missing for operator `<<`.
+      end
+    RUBY
+
+    expect_correction(<<~RUBY)
+      class << self
       end
     RUBY
   end