diff --git a/src/main/scala/scala/collection/immutable/next/package.scala b/src/main/scala/scala/collection/immutable/next/package.scala
new file mode 100644
index 0000000..8de7545
--- /dev/null
+++ b/src/main/scala/scala/collection/immutable/next/package.scala
@@ -0,0 +1,49 @@
+/*
+ * Scala (https://www.scala-lang.org)
+ *
+ * Copyright EPFL and Lightbend, Inc.
+ *
+ * Licensed under Apache License 2.0
+ * (http://www.apache.org/licenses/LICENSE-2.0).
+ *
+ * See the NOTICE file distributed with this work for
+ * additional information regarding copyright ownership.
+ */
+
+package scala.collection.immutable
+
+package object next {
+
+  implicit class NextLazyListExtensions[T](private val ll: LazyList[T]) extends AnyVal {
+    /**
+     * When called on a finite `LazyList`, returns a circular structure
+     * that endlessly repeats the elements in the input.
+     * The result is a true cycle occupying only constant memory.
+     *
+     * Does not force the input list (not even its empty-or-not status).
+     *
+     * Safe to call on unbounded input, but in that case the result is not a cycle
+     * (not even if the input was).
+     *
+     * Note that some `LazyList` methods preserve cyclicality and others do not.
+     * So for example the `tail` of a cycle is still a cycle, but `map` and `filter`
+     * on a cycle do not return cycles.
+     */
+    def cycle: LazyList[T] =
+      // case 1: the input is already known to be empty
+      // (the test can be changed to ll.knownIsEmpty when this code moves to stdlib)
+      if (ll.knownSize == 0) LazyList.empty
+      // we don't want to force the input's empty-or-not status until we must.
+      // `LazyList.empty #:::` accomplishes that delay
+      else LazyList.empty #::: {
+        // case 2: the input is later discovered to be empty
+        if (ll.isEmpty) LazyList.empty
+        else {
+          // case 3: non-empty
+          lazy val result: LazyList[T] = ll #::: result
+          result
+        }
+      }
+  }
+
+}
diff --git a/src/test/scala/scala/collection/immutable/TestLazyListExtensions.scala b/src/test/scala/scala/collection/immutable/TestLazyListExtensions.scala
new file mode 100644
index 0000000..c3e25af
--- /dev/null
+++ b/src/test/scala/scala/collection/immutable/TestLazyListExtensions.scala
@@ -0,0 +1,120 @@
+/*
+ * Scala (https://www.scala-lang.org)
+ *
+ * Copyright EPFL and Lightbend, Inc.
+ *
+ * Licensed under Apache License 2.0
+ * (http://www.apache.org/licenses/LICENSE-2.0).
+ *
+ * See the NOTICE file distributed with this work for
+ * additional information regarding copyright ownership.
+ */
+
+package scala.collection.immutable
+
+import org.junit.Assert._
+import org.junit.Test
+
+import next._
+
+class TestLazyListExtensions {
+
+  // This method will *not* terminate for non-cyclic infinite-sized collections.
+  // (It's kind of nasty to have tests whose failure mode is to hang, but I don't
+  // see an obvious alternative that doesn't involve copying code from LazyList.
+  // Perhaps this could be improved at the time this all gets merged into stdlib.)
+  def assertConstantMemory[T](xs: LazyList[T]): Unit =
+    // `force` does cycle detection, so if this terminates, the collection is
+    // either finite or a cycle
+    xs.force
+
+  @Test
+  def cycleEmpty1(): Unit = {
+    val xs = LazyList.empty  // realized
+    val cyc = xs.cycle
+    assertTrue(cyc.isEmpty)
+    assertTrue(cyc.size == 0)
+    assertEquals(Nil, cyc.toList)
+  }
+  @Test
+  def cycleEmpty2(): Unit = {
+    val xs = LazyList.empty #::: LazyList.empty  // not realized
+    assertEquals(-1, xs.knownSize)  // double-check it's not realized
+    val cyc = xs.cycle
+    assertTrue(cyc.isEmpty)
+    assertTrue(cyc.size == 0)
+    assertEquals(Nil, cyc.toList)
+  }
+  @Test
+  def cycleNonEmpty(): Unit = {
+    val xs = LazyList(1, 2, 3)
+    val cyc = xs.cycle
+    assertFalse(cyc.isEmpty)
+    assertConstantMemory(cyc)
+    assertEquals(LazyList(1, 2, 3, 1, 2, 3, 1, 2), cyc.take(8))
+  }
+  @Test
+  def cycleToString(): Unit = {
+    assertEquals("LazyList()",
+      LazyList.empty.cycle.toString)
+    assertEquals("LazyList(<not computed>)",
+      LazyList(1, 2, 3).cycle.toString)
+    // note cycle detection here!
+    assertEquals("LazyList(1, 2, 3, <cycle>)",
+      LazyList(1, 2, 3).cycle.force.toString)
+  }
+  @Test
+  def cycleRepeats(): Unit = {
+    val xs = LazyList(1, 2, 3)
+    val cyc = xs.cycle
+    assertFalse(cyc.isEmpty)
+    assertEquals(LazyList(1, 2, 3, 1, 2, 3, 1, 2), cyc.take(8))
+  }
+  @Test
+  def cycleConstantMemory1(): Unit = {
+    val xs = LazyList(1, 2, 3)
+    val cyc = xs.cycle
+    assertTrue(cyc.tail eq cyc.tail.tail.tail.tail)
+    assertTrue(cyc.tail.tail eq cyc.drop(4).tail)
+    assertTrue(cyc.tail eq cyc.drop(3).tail)
+  }
+  @Test
+  def cycleConstantMemory2(): Unit = {
+    var counter = 0
+    def count(): Int = { counter += 1; counter }
+    val xs = count() #:: count() #:: count() #:: LazyList.empty
+    val cyc = xs.cycle
+    assertEquals(0, counter)
+    assertEquals(10, cyc.take(10).size)
+    assertEquals(3, counter)
+  }
+  @Test
+  def cycleConstantMemory3(): Unit = {
+    val xs = LazyList(1, 2, 3)
+    val cyc = xs.cycle
+    assertConstantMemory(cyc)
+    assertConstantMemory(cyc.tail)
+    assertConstantMemory(cyc.tail.tail)
+    assertConstantMemory(cyc.tail.tail.tail)
+    assertConstantMemory(cyc.tail.tail.tail.tail)
+    assertConstantMemory(cyc.drop(1))
+    assertConstantMemory(cyc.drop(10))
+  }
+  @Test
+  def cycleUnbounded(): Unit = {
+    val xs = LazyList.from(1)
+    val cyc = xs.cycle
+    assertEquals(LazyList(1, 2, 3), cyc.take(3))
+  }
+  @Test
+  def cycleSecondCallIsSafeButNotIdempotent(): Unit = {
+    val xs = LazyList(1, 2, 3)
+    // this is safe to do
+    val twice = xs.cycle.cycle
+    // and the contents are as expected
+    assertEquals(LazyList(1, 2, 3, 1, 2, 3, 1, 2), twice.take(8))
+    // but the result is not a cycle. it might be nice if it were, but oh well.
+    // testing the existing behavior.
+    assertFalse(twice.tail eq twice.tail.tail.tail.tail)
+  }
+}