There is no direct connection from Chamonix to Val Thorens. However, you can take the taxi to Bourg-St.Maurice, take the train to Moutiers, then take the bus to Val Thorens. Alternatively, you can drive from Chamonix to Val Thorens in around 2 h 4 min.
How to get from Chamonix to Val Thorens
From Chamonix taxi to Bourg-St.Maurice, train to Moutiers, then bus to Val Thorens. 4 h 12 min 152€. From Chamonix drive to Val Thorens. 2 h 4 min 18€. From Chamonix Mont Blanc bus to Genève Aéroport, walk to Genève Airport, then shuttle to Val Thorens Arolles. 6 h 33 min 88€.