diff --git a/scripts/naming.py b/scripts/naming.py
index 6f02f31..1331bdb 100644
--- a/scripts/naming.py
+++ b/scripts/naming.py
@@ -26,12 +26,13 @@ def class_name(operation_id: str) -> str:
 def python_name(wire: str) -> str:
     """A query parameter's wire name as a keyword argument.
 
-    A leading `_` is dropped, `-` and `:` become `_`, and camelCase becomes snake_case:
+    A leading `_` is dropped, `-`, `:` and `.` become `_`, and camelCase becomes snake_case:
     `_count` is `count`, `name:contains` is `name_contains`, `address-city` is `address_city`,
-    `serviceTypeCode` is `service_type_code`.
+    `serviceTypeCode` is `service_type_code`, and a FHIR chained search such as
+    `location.address-state` is `location_address_state`.
     """
     name = wire[1:] if wire.startswith("_") else wire
-    name = re.sub(r"[-:]", "_", name)
+    name = re.sub(r"[-:.]", "_", name)
     name = _CAMEL.sub("_", name).lower()
     if not name.isidentifier() or keyword.iskeyword(name):
         raise ValueError(f"the query parameter {wire!r} has no Python name: {name!r}")
diff --git a/tests/test_encode.py b/tests/test_encode.py
index ffa0303..e4764da 100644
--- a/tests/test_encode.py
+++ b/tests/test_encode.py
@@ -98,6 +98,9 @@ def test_a_url_on_another_host_is_refused() -> None:
         ("displayLanguage", "display_language"),
         ("isVirtual", "is_virtual"),
         ("new-patient-from-network", "new_patient_from_network"),
+        # FHIR's chained search parameters, sent under their own names.
+        ("location.address-state", "location_address_state"),
+        ("organization.identifier", "organization_identifier"),
     ],
 )
 def test_wire_names_map_to_python_names(wire: str, python: str) -> None:
@@ -108,7 +111,7 @@ def test_a_name_python_cannot_take_is_refused() -> None:
     with pytest.raises(ValueError, match="no Python name"):
         naming.python_name("class")
     with pytest.raises(ValueError, match="no Python name"):
-        naming.python_name("a.b")
+        naming.python_name("a/b")
 
 
 def test_operation_ids_and_docs_slugs() -> None: