diff --git a/crates/polars-core/src/frame/mod.rs b/crates/polars-core/src/frame/mod.rs
index 2d264fe50115..52e41cf27c9f 100644
--- a/crates/polars-core/src/frame/mod.rs
+++ b/crates/polars-core/src/frame/mod.rs
@@ -464,6 +464,13 @@ impl DataFrame {
 
     /// Returns true if the chunks of the columns do not align and re-chunking should be done
     pub fn should_rechunk(&self) -> bool {
+        // Fast check. It is also needed for correctness, as code below doesn't check if the number
+        // of chunks is equal.
+        if !self.get_columns().iter().map(|s| s.n_chunks()).all_equal() {
+            return true;
+        }
+
+        // From here we check chunk lengths.
         let mut chunk_lengths = self.columns.iter().map(|s| s.chunk_lengths());
         match chunk_lengths.next() {
             None => false,
diff --git a/py-polars/tests/unit/test_chunks.py b/py-polars/tests/unit/test_chunks.py
new file mode 100644
index 000000000000..63e7a327f003
--- /dev/null
+++ b/py-polars/tests/unit/test_chunks.py
@@ -0,0 +1,16 @@
+import numpy as np
+
+import polars as pl
+
+
+def test_chunks_align_16830() -> None:
+    n = 2
+    df = pl.DataFrame(
+        {"index_1": np.repeat(np.arange(10), n), "index_2": np.repeat(np.arange(10), n)}
+    )
+    df = pl.concat([df[0:10], df[10:]], rechunk=False)
+    df = df.filter(df["index_1"] == 0)  # filter chunks
+    df = df.with_columns(
+        index_2=pl.Series(values=[0] * n)
+    )  # set a chunk of different size
+    df.set_sorted("index_2")  # triggers `select_chunk`.