Change AppendChain(...Constructor) to Extend(Constructor).
Add tests for Extend().

chain.go

diff --git a/chain.go b/chain.go
index f3afddf..d281ad3 100644
--- a/chain.go
+++ b/chain.go
@@ -93,14 +93,14 @@
 	return newChain
 }
 
-// AppendChain extends a chain, adding the specified chains
-// as the last ones in the request flow.
+// Extend extends a chain by adding the specified chain
+// as the last one in the request flow.
 //
-// AppendChain returns a new chain, leaving the original one untouched.
+// Extend returns a new chain, leaving the original one untouched.
 //
 //     stdChain := alice.New(m1, m2)
 //     ext1Chain := alice.New(m3, m4)
-//     ext2Chain := stdChain.AppendChain(ext1Chain)
+//     ext2Chain := stdChain.Extend(ext1Chain)
 //     // requests in stdChain go  m1 -> m2
 //     // requests in ext1Chain go m3 -> m4
 //     // requests in ext2Chain go m1 -> m2 -> m3 -> m4
@@ -111,13 +111,9 @@
 // 		csrf := nosurf.New(h)
 // 		csrf.SetFailureHandler(aHtmlAfterNosurf.ThenFunc(csrfFail))
 // 		return csrf
-// 	}).AppendChain(aHtmlAfterNosurf)
+// 	}).Extend(aHtmlAfterNosurf)
 //		// requests to aHtml hitting nosurfs success handler go m1 -> nosurf -> m2 -> target-handler
 //		// requests to aHtml hitting nosurfs failure handler go m1 -> nosurf -> m2 -> csrfFail
-func (c Chain) AppendChain(chains ...Chain) Chain {
-	newChain := c
-	for _, ch := range chains {
-		newChain = newChain.Append(ch.constructors...)
-	}
-	return newChain
+func (c Chain) Extend(chain Chain) Chain {
+	return c.Append(chain.constructors...)
 }

chain_test.go

diff --git a/chain_test.go b/chain_test.go
index f1cf749..49c0470 100644
--- a/chain_test.go
+++ b/chain_test.go
@@ -113,3 +113,32 @@
 
 	assert.NotEqual(t, &chain.constructors[0], &newChain.constructors[0])
 }
+
+func TestExtendAddsHandlersCorrectly(t *testing.T) {
+	chain1 := New(tagMiddleware("t1\n"), tagMiddleware("t2\n"))
+	chain2 := New(tagMiddleware("t3\n"), tagMiddleware("t4\n"))
+	newChain := chain1.Extend(chain2)
+
+	assert.Equal(t, len(chain1.constructors), 2)
+	assert.Equal(t, len(chain2.constructors), 2)
+	assert.Equal(t, len(newChain.constructors), 4)
+
+	chained := newChain.Then(testApp)
+
+	w := httptest.NewRecorder()
+	r, err := http.NewRequest("GET", "/", nil)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	chained.ServeHTTP(w, r)
+
+	assert.Equal(t, w.Body.String(), "t1\nt2\nt3\nt4\napp\n")
+}
+
+func TestExtendRespectsImmutability(t *testing.T) {
+	chain := New(tagMiddleware(""))
+	newChain := chain.Extend(New(tagMiddleware("")))
+
+	assert.NotEqual(t, &chain.constructors[0], &newChain.constructors[0])
+}