diff --git a/chatmastermind/chat.py b/chatmastermind/chat.py
index ddabb56..7c4dd35 100644
--- a/chatmastermind/chat.py
+++ b/chatmastermind/chat.py
@@ -62,7 +62,10 @@ def make_file_path(dir_path: Path,
     Create a file_path for the given directory using the
     given file_suffix and ID generator function.
     """
-    return dir_path / f"{next_fid():04d}{file_suffix}"
+    file_path = dir_path / f"{next_fid():04d}{file_suffix}"
+    while file_path.exists():
+        file_path = dir_path / f"{next_fid():04d}{file_suffix}"
+    return file_path
 
 
 def write_dir(dir_path: Path,