diff --git a/crates/polars-pipe/src/executors/sinks/joins/cross.rs b/crates/polars-pipe/src/executors/sinks/joins/cross.rs
index 9a0bb1fbab94..f48778c9f5cb 100644
--- a/crates/polars-pipe/src/executors/sinks/joins/cross.rs
+++ b/crates/polars-pipe/src/executors/sinks/joins/cross.rs
@@ -118,11 +118,13 @@ impl Operator for CrossJoinProbe {
                         let iter_right = self.in_process_right.as_mut().unwrap();
                         let offset = iter_right.next().unwrap();
                         let right_df = chunk.data.slice(offset as i64, size);
-                        let df = self.in_process_left_df.cross_join(
+                        let mut df = self.in_process_left_df.cross_join(
                             &right_df,
                             Some(self.suffix.as_ref()),
                             None,
                         )?;
+                        // Cross joins can produce multiple chunks.
+                        df.as_single_chunk_par();
                         Ok(OperatorResult::HaveMoreOutPut(chunk.with_data(df)))
                     },
                 }
@@ -135,7 +137,7 @@ impl Operator for CrossJoinProbe {
 
                 // we use the first join to determine the output names
                 // this we can amortize the name allocations.
-                let df = match &self.output_names {
+                let mut df = match &self.output_names {
                     None => {
                         let df = self.in_process_left_df.cross_join(
                             &right_df,
@@ -149,6 +151,8 @@ impl Operator for CrossJoinProbe {
                         .in_process_left_df
                         ._cross_join_with_names(&right_df, names)?,
                 };
+                // Cross joins can produce multiple chunks.
+                df.as_single_chunk_par();
 
                 Ok(OperatorResult::HaveMoreOutPut(chunk.with_data(df)))
             },
diff --git a/crates/polars-pipe/src/executors/sinks/sort/sink_multiple.rs b/crates/polars-pipe/src/executors/sinks/sort/sink_multiple.rs
index 4e7155c8b0de..e552ba576994 100644
--- a/crates/polars-pipe/src/executors/sinks/sort/sink_multiple.rs
+++ b/crates/polars-pipe/src/executors/sinks/sort/sink_multiple.rs
@@ -227,6 +227,7 @@ impl SortSinkMultiple {
             )
         };
 
+        debug_assert_eq!(column.chunks().len(), 1);
         // Safety: length is correct
         unsafe { chunk.data.with_column_unchecked(column) };
         Ok(())
diff --git a/crates/polars-pipe/src/operators/chunks.rs b/crates/polars-pipe/src/operators/chunks.rs
index 18cbe16a1fc1..4789eae6281f 100644
--- a/crates/polars-pipe/src/operators/chunks.rs
+++ b/crates/polars-pipe/src/operators/chunks.rs
@@ -10,13 +10,17 @@ pub struct DataChunk {
 
 impl DataChunk {
     pub(crate) fn new(chunk_index: IdxSize, data: DataFrame) -> Self {
+        // Check the invariant that all columns have a single chunk.
+        #[cfg(debug_assertions)]
+        {
+            for c in data.get_columns() {
+                assert_eq!(c.chunks().len(), 1);
+            }
+        }
         Self { chunk_index, data }
     }
     pub(crate) fn with_data(&self, data: DataFrame) -> Self {
-        DataChunk {
-            chunk_index: self.chunk_index,
-            data,
-        }
+        Self::new(self.chunk_index, data)
     }
     pub(crate) fn is_empty(&self) -> bool {
         self.data.height() == 0
diff --git a/py-polars/tests/unit/streaming/test_streaming_join.py b/py-polars/tests/unit/streaming/test_streaming_join.py
index 47760aaaefa8..68719711d546 100644
--- a/py-polars/tests/unit/streaming/test_streaming_join.py
+++ b/py-polars/tests/unit/streaming/test_streaming_join.py
@@ -95,3 +95,16 @@ def test_streaming_cross_join_empty() -> None:
     ).collect(streaming=True)
     assert out.shape == (0, 2)
     assert out.columns == ["col1", "col1_right"]
+
+
+def test_streaming_join_rechunk_12498() -> None:
+    rows = pl.int_range(0, 2)
+
+    a = pl.select(A=rows).lazy()
+    b = pl.select(B=rows).lazy()
+
+    q = a.join(b, how="cross")
+    assert q.collect(streaming=True).to_dict(as_series=False) == {
+        "A": [0, 1, 0, 1],
+        "B": [0, 0, 1, 1],
+    }