diff --git c/synapse/storage/databases/main/event_federation.py w/synapse/storage/databases/main/event_federation.py
index fb132ef09..97ac07c3a 100644
--- c/synapse/storage/databases/main/event_federation.py
+++ w/synapse/storage/databases/main/event_federation.py
@@ -280,16 +280,64 @@ class EventFederationWorkerStore(SignatureWorkerStore, EventsWorkerStore, SQLBas
 
         # Now we look up all links for the chains we have, adding chains that
         # are reachable from any event.
+        #
+        # This query is structured to first get all chain IDs reachable, and
+        # then pull out all links from those chains. This does pull out more
+        # rows than is strictly necessary, however there isn't a way of
+        # structuring the recursive part of query to pull out the links without
+        # also returning large quantities of redundant data (which can make it a
+        # lot slower).
+        sql = """
+            WITH RECURSIVE links(chain_id) AS (
+                SELECT
+                    DISTINCT origin_chain_id
+                FROM event_auth_chain_links WHERE %s
+                UNION
+                SELECT
+                    target_chain_id
+                FROM event_auth_chain_links
+                INNER JOIN links ON (chain_id = origin_chain_id)
+            )
+            SELECT
+                origin_chain_id, origin_sequence_number,
+                target_chain_id, target_sequence_number
+            FROM links
+            INNER JOIN event_auth_chain_links ON (chain_id = origin_chain_id)
+        """
 
         # A map from chain ID to max sequence number *reachable* from any event ID.
         chains: Dict[int, int] = {}
-        for links in self._get_chain_links(txn, set(event_chains.keys())):
+
+        # Add all linked chains reachable from initial set of chains.
+        chains_to_fetch = set(event_chains.keys())
+        while chains_to_fetch:
+            batch2 = tuple(itertools.islice(chains_to_fetch, 1000))
+            chains_to_fetch.difference_update(batch2)
+            clause, args = make_in_list_sql_clause(
+                txn.database_engine, "origin_chain_id", batch2
+            )
+            txn.execute(sql % (clause,), args)
+
+            links: Dict[int, List[Tuple[int, int, int]]] = {}
+
+            for (
+                origin_chain_id,
+                origin_sequence_number,
+                target_chain_id,
+                target_sequence_number,
+            ) in txn:
+                links.setdefault(origin_chain_id, []).append(
+                    (origin_sequence_number, target_chain_id, target_sequence_number)
+                )
+
             for chain_id in links:
                 if chain_id not in event_chains:
                     continue
 
                 _materialize(chain_id, event_chains[chain_id], links, chains)
 
+            chains_to_fetch.difference_update(chains)
+
         # Add the initial set of chains, excluding the sequence corresponding to
         # initial event.
         for chain_id, seq_no in event_chains.items():
@@ -579,16 +627,61 @@ class EventFederationWorkerStore(SignatureWorkerStore, EventsWorkerStore, SQLBas
 
         # Now we look up all links for the chains we have, adding chains that
         # are reachable from any event.
+        #
+        # This query is structured to first get all chain IDs reachable, and
+        # then pull out all links from those chains. This does pull out more
+        # rows than is strictly necessary, however there isn't a way of
+        # structuring the recursive part of query to pull out the links without
+        # also returning large quantities of redundant data (which can make it a
+        # lot slower).
+        sql = """
+            WITH RECURSIVE links(chain_id) AS (
+                SELECT
+                    DISTINCT origin_chain_id
+                FROM event_auth_chain_links WHERE %s
+                UNION
+                SELECT
+                    target_chain_id
+                FROM event_auth_chain_links
+                INNER JOIN links ON (chain_id = origin_chain_id)
+            )
+            SELECT
+                origin_chain_id, origin_sequence_number,
+                target_chain_id, target_sequence_number
+            FROM links
+            INNER JOIN event_auth_chain_links ON (chain_id = origin_chain_id)
+        """
+
+        # (We need to take a copy of `seen_chains` as we want to mutate it in
+        # the loop)
+        chains_to_fetch = set(seen_chains)
+        while chains_to_fetch:
+            batch2 = tuple(itertools.islice(chains_to_fetch, 1000))
+            clause, args = make_in_list_sql_clause(
+                txn.database_engine, "origin_chain_id", batch2
+            )
+            txn.execute(sql % (clause,), args)
+
+            links: Dict[int, List[Tuple[int, int, int]]] = {}
+
+            for (
+                origin_chain_id,
+                origin_sequence_number,
+                target_chain_id,
+                target_sequence_number,
+            ) in txn:
+                links.setdefault(origin_chain_id, []).append(
+                    (origin_sequence_number, target_chain_id, target_sequence_number)
+                )
 
-        # (We need to take a copy of `seen_chains` as the function mutates it)
-        for links in self._get_chain_links(txn, set(seen_chains)):
             for chains in set_to_chain:
                 for chain_id in links:
                     if chain_id not in chains:
                         continue
 
                     _materialize(chain_id, chains[chain_id], links, chains)
 
+                chains_to_fetch.difference_update(chains)
                 seen_chains.update(chains)
 
         # Now for each chain we figure out the maximum sequence number reachable