Add icon-visibility attribute to cr.ui.Tree.

chrome/browser/resources/shared/css/tree.css

 tree {
   outline: none;
   overflow: auto;
   display: block;
 }
 
 .tree-item > .tree-row {
   color: black;
   -webkit-user-select: none;
   border: 1px solid rgba(255,255,255,0); /* transparent white */
@@ skipping 82 matching lines @@
   display: none;
 }
 
 .tree-item > .tree-row > * {
   display: inline-block;
   box-sizing: border-box;
 }
 
 .tree-label {
   -webkit-padding-start: 20px;
-  background-image: url("../../../../../ui/resources/folder_closed.png");
   background-position: 0 50%;
   background-repeat: no-repeat;
   white-space: pre;
 }
 
+html[dir=rtl] .tree-label {
+  background-position: 100% 50%;
+}
+
+html[dir=rtl] .tree-label,
+html[dir=rtl] .tree-row[may-have-children] > .tree-label {
+  background-image: url("../../../../../ui/resources/folder_closed_rtl.png");
+}
+
+html[dir=rtl] .tree-item[expanded] > .tree-row > .tree-label {
+  background-image: url("../../../../../ui/resources/folder_open_rtl.png");
+}
+
+tree[icon-visibility=hidden] .tree-label {
+  -webkit-padding-start: 0;
+  background-image: none !important;
+}
+
+tree[icon-visibility=parent] .tree-label,
+tree[icon-visibility=parent] .tree-row[has-children=false] > .tree-label {
+  background-image: none;
+}
+
+.tree-label,
+.tree-row[may-have-children] > .tree-label {
+  background-image: url("../../../../../ui/resources/folder_closed.png");
+}
+
+.tree-item[expanded] > .tree-row > .tree-label {
+  background-image: url("../../../../../ui/resources/folder_open.png");
+}
+
 /* We need to ensure that even empty labels take up space */
 .tree-label:empty:after {
   content: " ";
   white-space: pre;
 }
 
 .tree-rename > .tree-row > .tree-label {
   -webkit-user-select: auto;
   -webkit-user-modify: read-write-plaintext-only;
   background: white;
   color: black;
   outline: 1px solid black;
 }
 
-html[dir=rtl] .tree-label {
-  background-position: 100% 50%;
-}
-
-.tree-item[expanded] > .tree-row > .tree-label {
-  background-image: url("../../../../../ui/resources/folder_open.png");
-}
-
-html[dir='rtl'] .tree-label {
-  background-image: url("../../../../../ui/resources/folder_closed_rtl.png");
-}
-
-html[dir='rtl'] .tree-item[expanded] > .tree-row > .tree-label {
-  background-image: url("../../../../../ui/resources/folder_open_rtl.png");
-}
-
 .tree-item[editing] input {
   /* Do not inherit the line-height */
   font-family: inherit;
   font-size: inherit;
   font-weight: inherit;
   margin: -2px -8px -2px -3px;
   padding: 1px 7px 1px 1px;
 }
 
 html:not([os=mac]) .tree-item[editing] input {
   outline: none;
 }
 
 html[dir=rtl] .tree-item[editing] input {
   margin: -2px -3px -2px -8px;
   padding: 1px 1px 1px 7px;
 }