diff --git a/outlines/models/openai.py b/outlines/models/openai.py
index 16126acb0..f87a26f7e 100644
--- a/outlines/models/openai.py
+++ b/outlines/models/openai.py
@@ -130,10 +130,14 @@ def __init__(
         self.client = openai.AsyncOpenAI(
             api_key=api_key, max_retries=max_retries, timeout=timeout
         )
-        self.total_tokens = 0
-        self.last_tokens: int
         self.system_prompt = system_prompt
 
+        # We count the total number of prompt and generated tokens as returned
+        # by the OpenAI API, summed over all the requests performed with this
+        # model instance.
+        self.prompt_tokens = 0
+        self.completion_tokens = 0
+
     def __call__(
         self,
         prompt: Union[str, List[str]],
@@ -170,10 +174,12 @@ def __call__(
                 )
             )
         if "gpt-" in self.config.model:
-            response, self.last_tokens = generate_chat(
+            response, usage = generate_chat(
                 prompt, self.system_prompt, self.client, config
             )
-            self.total_tokens += self.last_tokens
+            self.prompt_tokens += usage.prompt_tokens
+            self.completion_tokens += usage.completion_tokens
+
             return response
 
     def generate_choice(
@@ -227,10 +233,11 @@ def generate_choice(
 
             config = replace(config, logit_bias=mask, max_tokens=max_tokens_left)
 
-            response, self.last_tokens = generate_chat(
+            response, usage = generate_chat(
                 prompt, self.system_prompt, self.client, config
             )
-            self.total_tokens += self.last_tokens
+            self.completion_tokens += usage.completion_tokens
+            self.prompt_tokens += usage.completion_tokens
 
             encoded_response = tokenizer.encode(response)
 
@@ -283,12 +290,33 @@ async def generate_chat(
     client: "AsyncOpenAI",
     config: OpenAIConfig,
 ) -> Tuple[np.ndarray, "CompletionUsage"]:
+    """Call OpenAI's Chat Completion API.
+
+    Parameters
+    ----------
+    prompt
+        The prompt we use to start the generation. Passed to the model
+        with the "user" role.
+    system_prompt
+        The system prompt, passed to the model with the "system" role
+        before the prompt.
+    client
+        The API client
+    config
+        An `OpenAIConfig` instance.
+
+    Returns
+    -------
+    A tuple that contains the model's response(s) and usage statistics.
+
+    """
     system_message = (
         [{"role": "system", "content": system_prompt}] if system_prompt else []
     )
+    user_message = [{"role": "user", "content": prompt}]
 
     responses = await client.chat.completions.create(
-        messages=system_message + [{"role": "user", "content": prompt}],
+        messages=system_message + user_message,
         **asdict(config),  # type: ignore
     )