As of TypeScript 2 (or 2.x, not sure), you should import the Google Chrome types from @types.
In package.json:
"devDependencies": {
...
"@types/chrome": "0.0.35", // Or just npm install --save-dev @types/chrome
And in tsconfig:
"types": [
// (various types, e.g. jquery, core-js),
"chrome"
]