diff --git a/electrum/interface.py b/electrum/interface.py
index 3fc51e559..981f76aee 100644
--- a/electrum/interface.py
+++ b/electrum/interface.py
@@ -856,22 +856,47 @@ class Interface(Logger):
     async def _fast_forward_chain(
         self,
         *,
-        height: int,
-        tip: int,
-    ) -> Optional[Tuple[bool, int]]:
+        height: int,  # usually local chain tip + 1
+        tip: int,  # server tip. we should not request past this.
+    ) -> int:
+        """Request some headers starting at `height` to grow the blockchain of this interface.
+        Returns number of headers we managed to connect, starting at `height`.
+        """
         if not is_non_negative_integer(height):
             raise Exception(f"{repr(height)} is not a block height")
         if not is_non_negative_integer(tip):
             raise Exception(f"{repr(tip)} is not a block height")
-        index = height // CHUNK_SIZE
-        size = CHUNK_SIZE
-        size = min(size, tip - index * CHUNK_SIZE + 1)
-        size = max(size, 0)
-        headers = await self.get_block_headers(start_height=index * CHUNK_SIZE, count=size)
-        conn = self.blockchain.connect_chunk(index, data=b"".join(headers))
-        if not conn:
-            return conn, 0
-        return conn, len(headers)
+        if not (height > constants.net.max_checkpoint()
+                or height == 0 == constants.net.max_checkpoint()):
+            raise Exception(f"{height=} must be > cp={constants.net.max_checkpoint()}")
+        assert height <= tip, f"{height=} must be <= {tip=}"
+        # Request a few chunks of headers concurrently.
+        # tradeoffs:
+        # - more chunks: higher memory requirements
+        # - more chunks: higher concurrency => syncing needs fewer network round-trips
+        # - if a chunk does not connect, bandwidth for all later chunks is wasted
+        async with OldTaskGroup() as group:
+            tasks = []  # type: List[Tuple[int, asyncio.Task[Sequence[bytes]]]]
+            index0 = height // CHUNK_SIZE
+            for chunk_cnt in range(10):
+                index = index0 + chunk_cnt
+                start_height = index * CHUNK_SIZE
+                if start_height > tip:
+                    break
+                end_height = min(start_height + CHUNK_SIZE - 1, tip)
+                size = end_height - start_height + 1
+                tasks.append((index, await group.spawn(self.get_block_headers(start_height=start_height, count=size))))
+        # try to connect chunks
+        num_headers = 0
+        for index, task in tasks:
+            headers = task.result()
+            conn = self.blockchain.connect_chunk(index, data=b"".join(headers))
+            if not conn:
+                break
+            num_headers += len(headers)
+        # We started at a chunk boundary, instead of requested `height`. Need to correct for that.
+        offset = height - index0 * CHUNK_SIZE
+        return max(0, num_headers - offset)
 
     def is_main_server(self) -> bool:
         return (self.network.interface == self or
@@ -1035,10 +1060,9 @@ class Interface(Logger):
                 # We are far from the tip.
                 # It is more efficient to process headers in large batches (CPU/disk_usage/logging).
                 # (but this wastes a little bandwidth, if we are not on a chunk boundary)
-                # TODO we should request (some) chunks concurrently. would help when we are many chunks behind
-                could_connect, num_headers = await self._fast_forward_chain(
+                num_headers = await self._fast_forward_chain(
                     height=height, tip=next_height)
-                if not could_connect:
+                if num_headers == 0:
                     if height <= constants.net.max_checkpoint():
                         raise GracefulDisconnect('server chain conflicts with checkpoints or genesis')
                     last, height = await self.step(height)
@@ -1046,7 +1070,7 @@ class Interface(Logger):
                 # report progress to gui/etc
                 util.trigger_callback('blockchain_updated')
                 util.trigger_callback('network_updated')
-                height = (height // CHUNK_SIZE * CHUNK_SIZE) + num_headers
+                height += num_headers
                 assert height <= next_height+1, (height, self.tip)
                 last = ChainResolutionMode.CATCHUP
             else: