diff --git a/src/compiler/binder.ts b/src/compiler/binder.ts
index 1cff02ffc48..f92f6789d29 100644
--- a/src/compiler/binder.ts
+++ b/src/compiler/binder.ts
@@ -1910,6 +1910,17 @@ namespace ts {
                 // This is so that they can flow through PropertyName transforms unaffected.
                 // Instead, we mark the container as ES6, so that it can properly handle the transform.
                 transformFlags = TransformFlags.ContainsComputedPropertyName;
+                if (subtreeFlags & TransformFlags.ContainsLexicalThis) {
+                    // A computed method name like `[this.getName()](x: string) { ... }` needs to
+                    // distinguish itself from the normal case of a method body containing `this`:
+                    // `this` inside a method doesn't need to be rewritten (the method provides `this`),
+                    // whereas `this` inside a computed name *might* need to be rewritten if the class/object
+                    // is inside an arrow function:
+                    // `_this = this; () => class K { [_this.getName()]() { ... } }`
+                    // To make this distinction, use ContainsLexicalThisInComputedPropertyName
+                    // instead of ContainsLexicalThis for computed property names
+                    transformFlags |= TransformFlags.ContainsLexicalThisInComputedPropertyName;
+                }
                 break;
 
             case SyntaxKind.SpreadElementExpression:
@@ -1945,6 +1956,11 @@ namespace ts {
                     // is an ES6 node.
                     transformFlags = TransformFlags.AssertES6;
                 }
+                if (subtreeFlags & TransformFlags.ContainsLexicalThisInComputedPropertyName) {
+                    // A computed property name containing `this` might need to be rewritten,
+                    // so propagate the ContainsLexicalThis flag upward.
+                    transformFlags |= TransformFlags.ContainsLexicalThis;
+                }
                 break;
 
             case SyntaxKind.CallExpression:
@@ -2256,6 +2272,11 @@ namespace ts {
             || hasModifier(node, ModifierFlags.Export)) {
             transformFlags |= TransformFlags.AssertTypeScript;
         }
+        if (subtreeFlags & TransformFlags.ContainsLexicalThisInComputedPropertyName) {
+            // A computed property name containing `this` might need to be rewritten,
+            // so propagate the ContainsLexicalThis flag upward.
+            transformFlags |= TransformFlags.ContainsLexicalThis;
+        }
 
         return updateTransformFlags(node, subtreeFlags, transformFlags, TransformFlags.ClassExcludes);
     }
@@ -2272,6 +2293,11 @@ namespace ts {
                 | TransformFlags.ContainsDecorators)) {
             transformFlags |= TransformFlags.AssertTypeScript;
         }
+        if (subtreeFlags & TransformFlags.ContainsLexicalThisInComputedPropertyName) {
+            // A computed property name containing `this` might need to be rewritten,
+            // so propagate the ContainsLexicalThis flag upward.
+            transformFlags |= TransformFlags.ContainsLexicalThis;
+        }
 
         return updateTransformFlags(node, subtreeFlags, transformFlags, TransformFlags.ClassExcludes);
     }
diff --git a/src/compiler/types.ts b/src/compiler/types.ts
index 627b33f0d34..4c99417950d 100644
--- a/src/compiler/types.ts
+++ b/src/compiler/types.ts
@@ -2830,11 +2830,12 @@ namespace ts {
         ContainsPropertyInitializer = 1 << 10,
         ContainsLexicalThis = 1 << 11,
         ContainsCapturedLexicalThis = 1 << 12,
-        ContainsDefaultValueAssignments = 1 << 13,
-        ContainsParameterPropertyAssignments = 1 << 14,
-        ContainsSpreadElementExpression = 1 << 15,
-        ContainsComputedPropertyName = 1 << 16,
-        ContainsBlockScopedBinding = 1 << 17,
+        ContainsLexicalThisInComputedPropertyName = 1 << 13,
+        ContainsDefaultValueAssignments = 1 << 14,
+        ContainsParameterPropertyAssignments = 1 << 15,
+        ContainsSpreadElementExpression = 1 << 16,
+        ContainsComputedPropertyName = 1 << 17,
+        ContainsBlockScopedBinding = 1 << 18,
 
         HasComputedFlags = 1 << 31, // Transform flags have been computed.
 
@@ -2853,10 +2854,10 @@ namespace ts {
         FunctionExcludes = ContainsDecorators | ContainsDefaultValueAssignments | ContainsCapturedLexicalThis | ContainsLexicalThis | ContainsParameterPropertyAssignments | ContainsBlockScopedBinding,
         ConstructorExcludes = ContainsDefaultValueAssignments | ContainsLexicalThis | ContainsCapturedLexicalThis | ContainsBlockScopedBinding,
         MethodOrAccessorExcludes = ContainsDefaultValueAssignments | ContainsLexicalThis | ContainsCapturedLexicalThis | ContainsBlockScopedBinding,
-        ClassExcludes = ContainsDecorators | ContainsPropertyInitializer | ContainsLexicalThis | ContainsCapturedLexicalThis | ContainsComputedPropertyName | ContainsParameterPropertyAssignments,
+        ClassExcludes = ContainsDecorators | ContainsPropertyInitializer | ContainsLexicalThis | ContainsCapturedLexicalThis | ContainsComputedPropertyName | ContainsParameterPropertyAssignments | ContainsLexicalThisInComputedPropertyName,
         ModuleExcludes = ContainsDecorators | ContainsLexicalThis | ContainsCapturedLexicalThis | ContainsBlockScopedBinding,
         TypeExcludes = ~ContainsTypeScript,
-        ObjectLiteralExcludes = ContainsDecorators | ContainsComputedPropertyName,
+        ObjectLiteralExcludes = ContainsDecorators | ContainsComputedPropertyName | ContainsLexicalThisInComputedPropertyName,
         ArrayLiteralOrCallOrNewExcludes = ContainsSpreadElementExpression,
     }
 
diff --git a/tests/baselines/reference/computedPropertyNames29_ES5.js b/tests/baselines/reference/computedPropertyNames29_ES5.js
index af6f93c8ad9..966081ae035 100644
--- a/tests/baselines/reference/computedPropertyNames29_ES5.js
+++ b/tests/baselines/reference/computedPropertyNames29_ES5.js
@@ -18,7 +18,8 @@ var C = (function () {
         var _this = this;
         (function () {
             var obj = (_a = {},
-                _a[_this.bar()] = function () { },
+                _a[_this.bar()] = function () { } // needs capture
+            ,
                 _a);
             var _a;
         });
diff --git a/tests/baselines/reference/computedPropertyNames31_ES5.js b/tests/baselines/reference/computedPropertyNames31_ES5.js
index 86fb6655a27..2e38e2a131f 100644
--- a/tests/baselines/reference/computedPropertyNames31_ES5.js
+++ b/tests/baselines/reference/computedPropertyNames31_ES5.js
@@ -38,7 +38,8 @@ var C = (function (_super) {
         var _this = this;
         (function () {
             var obj = (_a = {},
-                _a[_super.prototype.bar.call(_this)] = function () { },
+                _a[_super.prototype.bar.call(_this)] = function () { } // needs capture
+            ,
                 _a);
             var _a;
         });