Proton rearrangement rates in hydrogen bond networks are dominated by classical activation and quantum tunneling at higher and lower temperatures, respectively. Calix[4]arene (C4A) has a square-ring network composed of four hydroxyl groups with the O center dot center dot center dot O length of similar to 0.265 nm. Calorimetry and dielectric relaxation measurements were applied to determination of the rates in the crystals of C4A and its deuteron analogue (C4A-d). The rearrangement rates in C4A-d exhibited Arrhenius dependence in the measured temperature range. On the other hand, the rates in C4A showed the same dependence as those in C4A-d above 200 K, deviated from this dependence at around 180 K, and became independent of temperature at around 10(-4) s(-1) below 100 K. This is the that the tunneling in the quadruple proton rearrangement proceeds at a very slow rate of 10(-4) s(-1). This evidenced first determination by calorimetry of the proton tunneling rate.