diff --git a/src/compiler/checker.ts b/src/compiler/checker.ts
index c9809acc781c2..7e43791dc51f2 100644
--- a/src/compiler/checker.ts
+++ b/src/compiler/checker.ts
@@ -47519,6 +47519,9 @@ export function createTypeChecker(host: TypeCheckerHost): TypeChecker {
                 return !sym.exports ? [] : nodeBuilder.symbolTableToDeclarationStatements(sym.exports, node, flags, tracker, bundled);
             },
             isImportRequiredByAugmentation,
+            isNameReferencingGlobalValueAtLocation: (name, location) => {
+                return resolveEntityName(factory.createIdentifier(name), SymbolFlags.Value, /*ignoreErrors*/ true, /*dontResolveAlias*/ undefined, location) === getGlobalSymbol(escapeLeadingUnderscores(name), SymbolFlags.Value, /*diagnostic*/ undefined);
+            },
         };
 
         function isImportRequiredByAugmentation(node: ImportDeclaration) {
diff --git a/src/compiler/emitter.ts b/src/compiler/emitter.ts
index d407dadc246ae..66963d1d7fe60 100644
--- a/src/compiler/emitter.ts
+++ b/src/compiler/emitter.ts
@@ -1182,6 +1182,7 @@ export const notImplementedResolver: EmitResolver = {
     isBindingCapturedByNode: notImplemented,
     getDeclarationStatementsForSourceFile: notImplemented,
     isImportRequiredByAugmentation: notImplemented,
+    isNameReferencingGlobalValueAtLocation: notImplemented,
 };
 
 /**
diff --git a/src/compiler/transformers/ts.ts b/src/compiler/transformers/ts.ts
index 00eb218342e00..72eb45599912c 100644
--- a/src/compiler/transformers/ts.ts
+++ b/src/compiler/transformers/ts.ts
@@ -1901,9 +1901,24 @@ export function transformTypeScript(context: TransformationContext) {
     function transformEnumMemberDeclarationValue(member: EnumMember): Expression {
         const value = resolver.getConstantValue(member);
         if (value !== undefined) {
-            return typeof value === "string" ? factory.createStringLiteral(value) :
-                value < 0 ? factory.createPrefixUnaryExpression(SyntaxKind.MinusToken, factory.createNumericLiteral(Math.abs(value))) :
-                factory.createNumericLiteral(value);
+            if (typeof value === "string") {
+                return factory.createStringLiteral(value);
+            }
+            if (Number.isNaN(value)) {
+                return resolver.isNameReferencingGlobalValueAtLocation("NaN", member)
+                    ? factory.createIdentifier("NaN")
+                    : factory.createBinaryExpression(factory.createNumericLiteral(0), SyntaxKind.SlashToken, factory.createNumericLiteral(0));
+            }
+            if (!isFinite(value)) {
+                if (resolver.isNameReferencingGlobalValueAtLocation("Infinity", member)) {
+                    return value < 0 ? factory.createPrefixUnaryExpression(SyntaxKind.MinusToken, factory.createIdentifier("Infinity")) : factory.createIdentifier("Infinity");
+                }
+                const dividend = value < 0 ? factory.createPrefixUnaryExpression(SyntaxKind.MinusToken, factory.createNumericLiteral(1)) : factory.createNumericLiteral(1);
+                return factory.createBinaryExpression(dividend, SyntaxKind.SlashToken, factory.createNumericLiteral(0));
+            }
+            return value < 0
+                ? factory.createPrefixUnaryExpression(SyntaxKind.MinusToken, factory.createNumericLiteral(Math.abs(value)))
+                : factory.createNumericLiteral(value);
         }
         else {
             enableSubstitutionForNonQualifiedEnumMembers();
diff --git a/src/compiler/types.ts b/src/compiler/types.ts
index 2096b177c5930..d1a15f152e67a 100644
--- a/src/compiler/types.ts
+++ b/src/compiler/types.ts
@@ -5634,6 +5634,7 @@ export interface EmitResolver {
     isBindingCapturedByNode(node: Node, decl: VariableDeclaration | BindingElement): boolean;
     getDeclarationStatementsForSourceFile(node: SourceFile, flags: NodeBuilderFlags, tracker: SymbolTracker, bundled?: boolean): Statement[] | undefined;
     isImportRequiredByAugmentation(decl: ImportDeclaration): boolean;
+    isNameReferencingGlobalValueAtLocation(name: string, location: Node): boolean;
 }
 
 // dprint-ignore
diff --git a/tests/baselines/reference/enumShadowedInfinityNaN2.js b/tests/baselines/reference/enumShadowedInfinityNaN2.js
new file mode 100644
index 0000000000000..ec47a6b130c2a
--- /dev/null
+++ b/tests/baselines/reference/enumShadowedInfinityNaN2.js
@@ -0,0 +1,28 @@
+//// [tests/cases/conformance/enums/enumShadowedInfinityNaN2.ts] ////
+
+//// [enumShadowedInfinityNaN2.ts]
+// repro https://github.com/microsoft/TypeScript/issues/55091
+
+let Infinity = 3;
+let NaN = 5;
+
+export enum A {
+    X = 1 / 0,
+    Y = -1 / 0,
+    B = 0 / 0,
+}
+
+
+//// [enumShadowedInfinityNaN2.js]
+"use strict";
+// repro https://github.com/microsoft/TypeScript/issues/55091
+Object.defineProperty(exports, "__esModule", { value: true });
+exports.A = void 0;
+var Infinity = 3;
+var NaN = 5;
+var A;
+(function (A) {
+    A[A["X"] = 1 / 0] = "X";
+    A[A["Y"] = -1 / 0] = "Y";
+    A[A["B"] = 0 / 0] = "B";
+})(A || (exports.A = A = {}));
diff --git a/tests/baselines/reference/enumShadowedInfinityNaN2.symbols b/tests/baselines/reference/enumShadowedInfinityNaN2.symbols
new file mode 100644
index 0000000000000..45f0be86a256c
--- /dev/null
+++ b/tests/baselines/reference/enumShadowedInfinityNaN2.symbols
@@ -0,0 +1,24 @@
+//// [tests/cases/conformance/enums/enumShadowedInfinityNaN2.ts] ////
+
+=== enumShadowedInfinityNaN2.ts ===
+// repro https://github.com/microsoft/TypeScript/issues/55091
+
+let Infinity = 3;
+>Infinity : Symbol(Infinity, Decl(enumShadowedInfinityNaN2.ts, 2, 3))
+
+let NaN = 5;
+>NaN : Symbol(NaN, Decl(enumShadowedInfinityNaN2.ts, 3, 3))
+
+export enum A {
+>A : Symbol(A, Decl(enumShadowedInfinityNaN2.ts, 3, 12))
+
+    X = 1 / 0,
+>X : Symbol(A.X, Decl(enumShadowedInfinityNaN2.ts, 5, 15))
+
+    Y = -1 / 0,
+>Y : Symbol(A.Y, Decl(enumShadowedInfinityNaN2.ts, 6, 14))
+
+    B = 0 / 0,
+>B : Symbol(A.B, Decl(enumShadowedInfinityNaN2.ts, 7, 15))
+}
+
diff --git a/tests/baselines/reference/enumShadowedInfinityNaN2.types b/tests/baselines/reference/enumShadowedInfinityNaN2.types
new file mode 100644
index 0000000000000..47d3b511610ea
--- /dev/null
+++ b/tests/baselines/reference/enumShadowedInfinityNaN2.types
@@ -0,0 +1,36 @@
+//// [tests/cases/conformance/enums/enumShadowedInfinityNaN2.ts] ////
+
+=== enumShadowedInfinityNaN2.ts ===
+// repro https://github.com/microsoft/TypeScript/issues/55091
+
+let Infinity = 3;
+>Infinity : number
+>3 : 3
+
+let NaN = 5;
+>NaN : number
+>5 : 5
+
+export enum A {
+>A : A
+
+    X = 1 / 0,
+>X : A.X
+>1 / 0 : number
+>1 : 1
+>0 : 0
+
+    Y = -1 / 0,
+>Y : A.Y
+>-1 / 0 : number
+>-1 : -1
+>1 : 1
+>0 : 0
+
+    B = 0 / 0,
+>B : A.B
+>0 / 0 : number
+>0 : 0
+>0 : 0
+}
+
diff --git a/tests/cases/conformance/enums/enumShadowedInfinityNaN2.ts b/tests/cases/conformance/enums/enumShadowedInfinityNaN2.ts
new file mode 100644
index 0000000000000..4da67acc7ec29
--- /dev/null
+++ b/tests/cases/conformance/enums/enumShadowedInfinityNaN2.ts
@@ -0,0 +1,10 @@
+// repro https://github.com/microsoft/TypeScript/issues/55091
+
+let Infinity = 3;
+let NaN = 5;
+
+export enum A {
+    X = 1 / 0,
+    Y = -1 / 0,
+    B = 0 / 0,
+}