How do I send an HTTP GET request from a Chrome extension?

First, you'll need to edit your manifest.json and add the permission for www.example.com:

• For the new Manifest V3, use the host_permissions field:

  {
      "manifest_version": 3,
      ...
      "host_permissions": [
          "https://www.example.com/*"
      ],
      ...
  }
  

• If you are still using the old Manifest V2, use the permissions field:

  {
      "manifest_version": 2,
      ...
      "permissions": [
          "https://www.example.com/*"
      ],
      ...
  }
  

Then in your background page (or somewhere else) you can do:

fetch('http://www.example.com?par=0').then(r => r.text()).then(result => {
    // Result now contains the response text, do what you want...
})

See also MDN doc for fetch().

Deprecated version using XMLHttpRequest (ES5):

function callback() {
    if (xhr.readyState === XMLHttpRequest.DONE) {
        if (xhr.status === 200) {
            result = xhr.responseText;
            // ...
        }
    }
};

var xhr = new XMLHttpRequest();
xhr.open("GET", "http://www.example.com?par=0", true);
xhr.onreadystatechange = callback;
xhr.send();

NOTE the warning at the top of the relative documentation page:

In Manifest V3, XMLHttpRequest is not supported in background pages (provided by Service Workers). Please consider using its modern replacement, fetch()