diff --git a/storage/local/chunk/varbit.go b/storage/local/chunk/varbit.go
index 2ec59efd34..2b13d57d9c 100644
--- a/storage/local/chunk/varbit.go
+++ b/storage/local/chunk/varbit.go
@@ -1040,7 +1040,7 @@ func (it *varbitChunkIterator) FindAtOrBefore(t model.Time) bool {
 		prevT = model.Earliest
 		prevV model.SampleValue
 	)
-	for it.Scan() && t.After(it.t) {
+	for it.Scan() && !t.Before(it.t) {
 		prevT = it.t
 		prevV = it.v
 		// TODO(beorn7): If we are in a repeat, we could iterate forward
diff --git a/storage/local/storage_test.go b/storage/local/storage_test.go
index 2ff4c26861..da6d496493 100644
--- a/storage/local/storage_test.go
+++ b/storage/local/storage_test.go
@@ -980,6 +980,28 @@ func testValueAtOrBeforeTime(t *testing.T, encoding chunk.Encoding) {
 	if expected.Value != actual.Value {
 		t.Errorf("3.2. Got %v; want %v", actual.Value, expected.Value)
 	}
+
+	// #4 Query alternatingly exactly on and just between timestamps.
+	// Exposes issue #2965.
+	for i, expected := range samples {
+		i *= 2
+		actual := it.ValueAtOrBeforeTime(expected.Timestamp)
+		if expected.Timestamp != actual.Timestamp {
+			t.Errorf("4.%d. Got %v; want %v", i, actual.Timestamp, expected.Timestamp)
+		}
+		if expected.Value != actual.Value {
+			t.Errorf("4.%d. Got %v; want %v", i, actual.Value, expected.Value)
+		}
+
+		i++
+		actual = it.ValueAtOrBeforeTime(expected.Timestamp + 1)
+		if expected.Timestamp != actual.Timestamp {
+			t.Errorf("4.%d. Got %v; want %v", i, actual.Timestamp, expected.Timestamp)
+		}
+		if expected.Value != actual.Value {
+			t.Errorf("4.%d. Got %v; want %v", i, actual.Value, expected.Value)
+		}
+	}
 }
 
 func TestValueAtTimeChunkType0(t *testing.T) {