diff --git a/lib/components/modal-overlay.react.js b/lib/components/modal-overlay.react.js
--- a/lib/components/modal-overlay.react.js
+++ b/lib/components/modal-overlay.react.js
@@ -1,5 +1,6 @@
 // @flow
 
+import FocusTrap from 'focus-trap-react';
 import * as React from 'react';
 
 import css from './modal-overlay.css';
@@ -10,6 +11,10 @@
   +backgroundColor?: string,
 };
 
+const focusTrapOptions = {
+  fallbackFocus: '#modal-overlay',
+};
+
 function ModalOverlay(props: ModalOverlayProps): React.Node {
   const {
     children,
@@ -59,17 +64,20 @@
   );
 
   return (
-    <div
-      className={css.modalOverlay}
-      ref={overlayRef}
-      onMouseDown={onBackgroundMouseDown}
-      onMouseUp={onBackgroundMouseUp}
-      tabIndex={0}
-      onKeyDown={onKeyDown}
-      style={containerStyle}
-    >
-      {children}
-    </div>
+    <FocusTrap focusTrapOptions={focusTrapOptions}>
+      <div
+        id="modal-overlay"
+        className={css.modalOverlay}
+        ref={overlayRef}
+        onMouseDown={onBackgroundMouseDown}
+        onMouseUp={onBackgroundMouseUp}
+        tabIndex={-1}
+        onKeyDown={onKeyDown}
+        style={containerStyle}
+      >
+        {children}
+      </div>
+    </FocusTrap>
   );
 }
 
diff --git a/lib/flow-typed/npm/focus-trap-react_vx.x.x.js b/lib/flow-typed/npm/focus-trap-react_vx.x.x.js
new file mode 100644
--- /dev/null
+++ b/lib/flow-typed/npm/focus-trap-react_vx.x.x.js
@@ -0,0 +1,61 @@
+// flow-typed signature: 29231f6b72f5876f5692b592dce3c754
+// flow-typed version: <<STUB>>/focus-trap-react_v10.1.4/flow_v0.182.0
+
+/**
+ * This is an autogenerated libdef stub for:
+ *
+ *   'focus-trap-react'
+ *
+ * Fill this stub out by replacing all the `any` types.
+ *
+ * Once filled out, we encourage you to share your work with the
+ * community by sending a pull request to:
+ * https://github.com/flowtype/flow-typed
+ */
+
+declare module 'focus-trap-react' {
+  import type { Node } from 'react';
+
+  declare type FocusTargetValue = HTMLElement | string;
+  declare type FocusTargetValueOrFalse = FocusTargetValue | false;
+
+  declare type FocusTarget = FocusTargetValue | (() => FocusTargetValue);
+  declare type FocusTargetOrFalse = FocusTargetValueOrFalse | (() => FocusTargetValueOrFalse);
+
+  declare type MouseEventToBoolean = (event: MouseEvent | TouchEvent) => boolean;
+  declare type KeyboardEventToBoolean = (event: KeyboardEvent) => boolean;
+
+  declare type FocusTrapOptions = {
+    onActivate?: () => void,
+    onPostActivate?: () => void,
+    onPause?: () => void,
+    onPostPause?: () => void,
+    onUnpause?: () => void,
+    onPostUnpause?: () => void,
+    onDeactivate?: () => void,
+    onPostDeactivate?: () => void,
+    checkCanReturnFocus?: (trigger: HTMLElement) => Promise<void>,
+    initialFocus?: FocusTargetOrFalse,
+    fallbackFocus?: FocusTarget,
+    returnFocusOnDeactivate?: boolean,
+    setReturnFocus?: FocusTargetValueOrFalse | ((nodeFocusedBeforeActivation: HTMLElement) => FocusTargetValueOrFalse),
+    escapeDeactivates?: boolean | KeyboardEventToBoolean,
+    clickOutsideDeactivates?: boolean | MouseEventToBoolean,
+    allowOutsideClick?: boolean | MouseEventToBoolean,
+    preventScroll?: boolean,
+    delayInitialFocus?: boolean,
+    document?: Document,
+    isKeyForward?: KeyboardEventToBoolean,
+    isKeyBackward?: KeyboardEventToBoolean,
+  };
+
+  declare type FocusTrapProps = {
+    +children?: Node,
+    +active?: boolean,
+    +paused?: boolean,
+    +focusTrapOptions?: FocusTrapOptions,
+    +containerElements?: $ReadOnlyArray<HTMLElement>,
+  };
+
+  declare module.exports: FocusTrapProps => Node;
+}
diff --git a/lib/package.json b/lib/package.json
--- a/lib/package.json
+++ b/lib/package.json
@@ -41,6 +41,7 @@
     "ethers": "^5.7.2",
     "fast-json-stable-stringify": "^2.0.0",
     "file-type": "^12.3.0",
+    "focus-trap-react": "^10.1.4",
     "invariant": "^2.2.4",
     "just-clone": "^3.2.1",
     "lodash": "^4.17.21",
diff --git a/yarn.lock b/yarn.lock
--- a/yarn.lock
+++ b/yarn.lock
@@ -11776,6 +11776,21 @@
   dependencies:
     imul "^1.0.0"
 
+focus-trap-react@^10.1.4:
+  version "10.1.4"
+  resolved "https://registry.yarnpkg.com/focus-trap-react/-/focus-trap-react-10.1.4.tgz#bab7ea87aecfa2f7eb6f2fcc4be1e7311893ca17"
+  integrity sha512-vLUQRXI6SUJD8YLYTBa1DlCYRmTKFDxRvc4TEe2nq8S1aj+YKsucuNxqZUOf0+RZ01Yoiwtk/6rD9xqSvawIvQ==
+  dependencies:
+    focus-trap "^7.4.3"
+    tabbable "^6.1.2"
+
+focus-trap@^7.4.3:
+  version "7.4.3"
+  resolved "https://registry.yarnpkg.com/focus-trap/-/focus-trap-7.4.3.tgz#a3dae73d44df359eb92bbf37b18e173e813b16c5"
+  integrity sha512-BgSSbK4GPnS2VbtZ50VtOv1Sti6DIkj3+LkVjiWMNjLeAp1SH1UlLx3ULu/DCu4vq5R4/uvTm+zrvsMsuYmGLg==
+  dependencies:
+    tabbable "^6.1.2"
+
 follow-redirects@^1.0.0:
   version "1.14.8"
   resolved "https://registry.yarnpkg.com/follow-redirects/-/follow-redirects-1.14.8.tgz#016996fb9a11a100566398b1c6839337d7bfa8fc"
@@ -22197,6 +22212,11 @@
   resolved "https://registry.yarnpkg.com/symbol-tree/-/symbol-tree-3.2.4.tgz#430637d248ba77e078883951fb9aa0eed7c63fa2"
   integrity sha512-9QNk5KwDF+Bvz+PyObkmSYjI5ksVUYtjW7AU22r2NKcfLJcXp96hkDWU3+XndOsUb+AQ9QhfzfCT2O+CNWT5Tw==
 
+tabbable@^6.1.2:
+  version "6.1.2"
+  resolved "https://registry.yarnpkg.com/tabbable/-/tabbable-6.1.2.tgz#b0d3ca81d582d48a80f71b267d1434b1469a3703"
+  integrity sha512-qCN98uP7i9z0fIS4amQ5zbGBOq+OSigYeGvPy7NDk8Y9yncqDZ9pRPgfsc2PJIVM9RrJj7GIfuRgmjoUU9zTHQ==
+
 table@^5.4.6:
   version "5.4.6"
   resolved "https://registry.yarnpkg.com/table/-/table-5.4.6.tgz#1292d19500ce3f86053b05f0e8e7e4a3bb21079e"