We present results for the fluctuation-induced paraconductivity in YBa2Cu3P6.9 observed in the range T-C<T<130K. For the conductivity along the a-direction, we find that the deviation from the perfectly linear behaviour of rho(T) (above 130K) cannot be described by the standard models [Aslamasov-Larkin (AL), Lawrence-Doniach (LD), Maki-Thompson]. Empirically, the measured excess conductivity exhibits two regimes in T-T-C, respectively 1-7K and 7-35K, each displaying a different power-law. The paraconductivity along the b-axis is less pronounced, pointing to an effect of the CuO chains. Using a simple model of parallel conduction in the planes and along the chains, we obtain a well-defined fluctuation regime for the chain conductivity, most likely caused by proximity effect. The impact of fluctuations on the chains is noticeable only below 100K, roughly where the plane paraconductivity changes regime, supporting the view of a 2D to 3D crossover.