diff --git a/packages/@aws-cdk/aws-cloudfront/README.md b/packages/@aws-cdk/aws-cloudfront/README.md
index c13af4ace9e05..7865d7881fda6 100644
--- a/packages/@aws-cdk/aws-cloudfront/README.md
+++ b/packages/@aws-cdk/aws-cloudfront/README.md
@@ -97,7 +97,9 @@ new cloudfront.Distribution(this, 'myDist', {
 When you create a distribution, CloudFront assigns a domain name for the distribution, for example: `d111111abcdef8.cloudfront.net`; this value can
 be retrieved from `distribution.distributionDomainName`. CloudFront distributions use a default certificate (`*.cloudfront.net`) to support HTTPS by
 default. If you want to use your own domain name, such as `www.example.com`, you must associate a certificate with your distribution that contains
-your domain name. The certificate must be present in the AWS Certificate Manager (ACM) service in the US East (N. Virginia) region; the certificate
+your domain name, and provide one (or more) domain names from the certificate for the distribution.
+
+The certificate must be present in the AWS Certificate Manager (ACM) service in the US East (N. Virginia) region; the certificate
 may either be created by ACM, or created elsewhere and imported into ACM. When a certificate is used, the distribution will support HTTPS connections
 from SNI only and a minimum protocol version of TLSv1.2_2018.
 
@@ -108,6 +110,7 @@ const myCertificate = new acm.DnsValidatedCertificate(this, 'mySiteCert', {
 });
 new cloudfront.Distribution(this, 'myDist', {
   defaultBehavior: { origin: new origins.S3Origin(myBucket) },
+  domainNames: ['www.example.com'],
   certificate: myCertificate,
 });
 ```
diff --git a/packages/@aws-cdk/aws-cloudfront/lib/distribution.ts b/packages/@aws-cdk/aws-cloudfront/lib/distribution.ts
index b600c9177b2d4..de2316ad245ac 100644
--- a/packages/@aws-cdk/aws-cloudfront/lib/distribution.ts
+++ b/packages/@aws-cdk/aws-cloudfront/lib/distribution.ts
@@ -101,6 +101,17 @@ export interface DistributionProps {
    */
   readonly defaultRootObject?: string;
 
+  /**
+   * Alternative domain names for this distribution.
+   *
+   * If you want to use your own domain name, such as www.example.com, instead of the cloudfront.net domain name,
+   * you can add an alternate domain name to your distribution. If you attach a certificate to the distribution,
+   * you must add (at least one of) the domain names of the certificate to this list.
+   *
+   * @default - The distribution will only support the default generated name (e.g., d111111abcdef8.cloudfront.net)
+   */
+  readonly domainNames?: string[];
+
   /**
    * Enable or disable the distribution.
    *
@@ -239,6 +250,10 @@ export class Distribution extends Resource implements IDistribution {
       if (!Token.isUnresolved(certificateRegion) && certificateRegion !== 'us-east-1') {
         throw new Error(`Distribution certificates must be in the us-east-1 region and the certificate you provided is in ${certificateRegion}.`);
       }
+
+      if ((props.domainNames ?? []).length === 0) {
+        throw new Error('Must specify at least one domain name to use a certificate with a distribution');
+      }
     }
 
     const originId = this.addOrigin(props.defaultBehavior.origin);
@@ -258,6 +273,7 @@ export class Distribution extends Resource implements IDistribution {
         origins: Lazy.anyValue({ produce: () => this.renderOrigins() }),
         originGroups: Lazy.anyValue({ produce: () => this.renderOriginGroups() }),
         defaultCacheBehavior: this.defaultBehavior._renderBehavior(),
+        aliases: props.domainNames,
         cacheBehaviors: Lazy.anyValue({ produce: () => this.renderCacheBehaviors() }),
         comment: props.comment,
         customErrorResponses: this.renderErrorResponses(),
diff --git a/packages/@aws-cdk/aws-cloudfront/test/distribution.test.ts b/packages/@aws-cdk/aws-cloudfront/test/distribution.test.ts
index d0105db39f9d2..71b547e862553 100644
--- a/packages/@aws-cdk/aws-cloudfront/test/distribution.test.ts
+++ b/packages/@aws-cdk/aws-cloudfront/test/distribution.test.ts
@@ -51,6 +51,7 @@ test('exhaustive example of props renders correctly', () => {
     certificate,
     comment: 'a test',
     defaultRootObject: 'index.html',
+    domainNames: ['example.com'],
     enabled: false,
     enableIpv6: false,
     enableLogging: true,
@@ -64,6 +65,7 @@ test('exhaustive example of props renders correctly', () => {
 
   expect(stack).toHaveResource('AWS::CloudFront::Distribution', {
     DistributionConfig: {
+      Aliases: ['example.com'],
       DefaultCacheBehavior: {
         ForwardedValues: { QueryString: false },
         TargetOriginId: 'StackMyDistOrigin1D6D5E535',
@@ -263,16 +265,37 @@ describe('certificates', () => {
     }).toThrow(/Distribution certificates must be in the us-east-1 region and the certificate you provided is in eu-west-1./);
   });
 
-  test('adding a certificate renders the correct ViewerCertificate property', () => {
+  test('adding a certificate without a domain name throws', () => {
+    const certificate = acm.Certificate.fromCertificateArn(stack, 'Cert', 'arn:aws:acm:us-east-1:123456789012:certificate/12345678-1234-1234-1234-123456789012');
+
+    expect(() => {
+      new Distribution(stack, 'Dist1', {
+        defaultBehavior: { origin: defaultOrigin() },
+        certificate,
+      });
+    }).toThrow(/Must specify at least one domain name/);
+
+    expect(() => {
+      new Distribution(stack, 'Dist2', {
+        defaultBehavior: { origin: defaultOrigin() },
+        domainNames: [],
+        certificate,
+      });
+    }).toThrow(/Must specify at least one domain name/);
+  });
+
+  test('adding a certificate and domain renders the correct ViewerCertificate and Aliases property', () => {
     const certificate = acm.Certificate.fromCertificateArn(stack, 'Cert', 'arn:aws:acm:us-east-1:123456789012:certificate/12345678-1234-1234-1234-123456789012');
 
     new Distribution(stack, 'Dist', {
       defaultBehavior: { origin: defaultOrigin() },
+      domainNames: ['example.com', 'www.example.com'],
       certificate,
     });
 
     expect(stack).toHaveResourceLike('AWS::CloudFront::Distribution', {
       DistributionConfig: {
+        Aliases: ['example.com', 'www.example.com'],
         ViewerCertificate: {
           AcmCertificateArn: 'arn:aws:acm:us-east-1:123456789012:certificate/12345678-1234-1234-1234-123456789012',
           SslSupportMethod: 'sni-only',