For the 24 hours to 23:00 GMT, the USD rose 0.3% against the CHF and closed at 0.9988.
In economic news, Switzerland's total sight deposits advanced to a level of CHF557.2 billion in the week ended 17 March, from CHF555.4 billion in the previous week.
In the Asian session, at GMT0400, the pair is trading at 0.9987, with the USD trading marginally lower against the CHF from yesterday's close.
The pair is expected to find support at 0.9959, and a fall through could take it to the next support level of 0.9932. The pair is expected to find its first resistance at 1.0008, and a rise through could take it to the next resistance level of 1.0030.
Going ahead, traders would keep a close watch on Switzerland's trade balance for February and the SECO economic forecast report, slated to release in a while.
The currency pair is showing convergence with its 20 Hr moving average and trading above its 50 Hr moving average.