This work aims at studying in-line bubble coalescence in non-Newtonian fluids. The visualisation and power spectrum of time series data, recorded via an optical sensing device, confirm that the bubble formation at the orifice is perfectly periodic under a constant gas flowrate. However, the separation interval between bubbles becomes irregular during rise, until, at a certain height above the orifice, the coalescence occurs. An original approach is elaborated by relating the rise of a chain of bubbles to consecutive shear deformations. A series of measurements on a rheometer proves for the first time that the bubble coalescence is mainly governed by the dynamical competition between the creation and relaxation of shear stresses. The time delay embedding method of reconstructing the phase-space diagram is applied to time series data recorded at different heights in the bubble column. The calculation of several parameters : the largest Lyapunov exponent, the correlation dimension, the power spectrum, and the phase portraits, reveals that the coalescence between bubbles obeys a chaotic and deterministic mechanism.