diff --git a/src/black/__init__.py b/src/black/__init__.py
index a7e89ccba61..4eef16903c7 100644
--- a/src/black/__init__.py
+++ b/src/black/__init__.py
@@ -2083,6 +2083,15 @@ def visit_STRING(self, leaf: Leaf) -> Iterator[Line]:
         ) and is_multiline_string(leaf):
             prefix = "    " * self.current_line.depth
             docstring = fix_docstring(leaf.value[3:-3], prefix)
+            quote_char = leaf.value[0]
+            if len(docstring) > 0 and docstring[-1] == quote_char:
+                # This may have trimmed trailing whitespace, which may
+                # have produced four quotes in a row.  Escape the last
+                # quote -- if it isn't already, by being preceded by
+                # an odd number of backslashes
+                docstring = re.compile(rf"(([^\\]|^)(\\\\)*){quote_char}$").sub(
+                    rf"\1\\{quote_char}", docstring
+                )
             leaf.value = leaf.value[0:3] + docstring + leaf.value[-3:]
             normalize_string_quotes(leaf)
 
diff --git a/tests/data/docstring.py b/tests/data/docstring.py
index f5adeb7bb7b..c88733ae980 100644
--- a/tests/data/docstring.py
+++ b/tests/data/docstring.py
@@ -73,6 +73,38 @@ def single_line():
     """
     pass
 
+
+def containing_quotes():
+    """No quotes here
+
+    "quotes here" """
+    pass
+
+
+def containing_unbalanced_quotes():
+    """No quotes here
+
+    quote here" """
+    pass
+
+
+def entirely_space():
+    """
+      
+    """
+    pass
+
+
+def just_quote():
+    """ " """
+    pass
+
+
+def escaped_already():
+    """
+    foo\""""
+    pass
+
 # output
 
 class MyClass:
@@ -148,3 +180,33 @@ def over_indent():
 def single_line():
     """But with a newline after it!"""
     pass
+
+
+def containing_quotes():
+    """No quotes here
+
+    "quotes here\""""
+    pass
+
+
+def containing_unbalanced_quotes():
+    """No quotes here
+
+    quote here\""""
+    pass
+
+
+def entirely_space():
+    """"""
+    pass
+
+
+def just_quote():
+    """ " """
+    pass
+
+
+def escaped_already():
+    """
+    foo\""""
+    pass