We have measured the specific heat, C, of the easy-axis triangular lattice antiferromagnet CsNiCl3 in order to investigate the critical behavior associated with a multicritical point when the chiral symmetry is induced by an external magnetic field B. Critical exponents alpha determined from C are close to zero for two successive zero-field transitions, while alpha = 0.25 +/- 0.08 near the multicritical point at T(M) almost-equal-to 4.48 K and B(M) almost-equal-to 2.25 T, and alpha = 0.37 +/- 0.08 at the high-field phase boundary (B=6 T) far away from B(M). The observed crossover from ordinary XY behavior for B < B(M) to n = 3 chiral behavior at B(M) and finally to n = 2 chiral behavior for B >> B(M) is in very good agreement with recent theoretical predictions.