Remove zest from limes with a vegetable peeler and save fruit for another use. Put zest in a 1-qt.* glass jar or decorative bottle. Pour in gin (through a funnel, if the bottle has a narrow opening).
Close jar tightly and put in a cool, dark place for 1 week. The zest will lose its color almost immediately, but will continue to give flavor to the tequila.
Chill tequila and serve cold; it will gradually intensify and get a little cloudy.
* You can use a smaller bottle, but the infusion will be stronger, so taste it occasionally and remove the zest when the liquor tastes the way you want.
Make ahead: Up to 3 months (1 year, strained), chilled.