Aligning observed and modeled behavior is a central task in conformance checking. We propose a novel approach to alignments in the setting of stochastic timed process models, where transitions fire after an exponentially distributed random delay. In the spirit of alignments based on combinations of log moves and model moves, we propose a setting where the alignment may suggest adjustments of the observed timestamps (considering that they might have been recorded with errors) in order to make it closer to the most likely trace that the model, according to its stochastic parameters, can produce.