diff --git a/django/db/models/sql/query.py b/django/db/models/sql/query.py
index 256cbef8e14..403968e1183 100644
--- a/django/db/models/sql/query.py
+++ b/django/db/models/sql/query.py
@@ -1403,6 +1403,9 @@ class BaseQuery(object):
             field_name = field_list[0]
             col = field_name
             source = self.aggregates[field_name]
+            if not is_summary:
+                raise FieldError("Cannot compute %s('%s'): '%s' is an aggregate" % (
+                    aggregate.name, field_name, field_name))
         elif ((len(field_list) > 1) or
             (field_list[0] not in [i.name for i in opts.fields]) or
             self.group_by is None or
diff --git a/tests/regressiontests/aggregation_regress/models.py b/tests/regressiontests/aggregation_regress/models.py
index 3ce0f6e75d2..a6f99a997d7 100644
--- a/tests/regressiontests/aggregation_regress/models.py
+++ b/tests/regressiontests/aggregation_regress/models.py
@@ -297,6 +297,11 @@ FieldError: Cannot resolve keyword 'foo' into field. Choices are: authors, conta
 >>> HardbackBook.objects.annotate(n_authors=Count('authors')).values('name','n_authors')
 [{'n_authors': 2, 'name': u'Artificial Intelligence: A Modern Approach'}, {'n_authors': 1, 'name': u'Paradigms of Artificial Intelligence Programming: Case Studies in Common Lisp'}]
 
+# Regression for #10766 - Shouldn't be able to reference an aggregate fields in an an aggregate() call.
+>>> Book.objects.all().annotate(mean_age=Avg('authors__age')).annotate(Avg('mean_age'))
+Traceback (most recent call last):
+...
+FieldError: Cannot compute Avg('mean_age'): 'mean_age' is an aggregate
 
 """
 }