diff --git a/alloc/chunked.cpp b/alloc/chunked.cpp
index ee6a1edb..b87d5092 100644
--- a/alloc/chunked.cpp
+++ b/alloc/chunked.cpp
@@ -64,7 +64,13 @@ chunked::do_allocate (std::size_t size, std::size_t alignment)
     }
 
     // No chunk was found. We need to allocate a new chunk of at least enough size.
-    unimplemented ();
+    std::size_t allocation_size = cruft::max (size + alignment, m_chunk);
+    std::unique_ptr<std::byte[]> ptr (new std::byte[allocation_size]);
+    m_data.push_back (arena { ptr.get () });
+    m_data.back ().node->size = allocation_size;
+    m_data.back ().node->next = m_data.back ().node;
+    ptr.release ();
+    return do_allocate (size, alignment);
 }