Context : Aims : PSR J0855 - 4644 is a fast-spinning , energetic pulsar discovered at radio wavelengths near the south-eastern rim of the supernova remnant RX J0852.0 - 4622 . A follow-up XMM-Newton observation revealed the pulsar ’ s X-ray counterpart and a slightly asymmetric pulsar wind nebula suggesting possible jet structures . Lying at a distance d \leq 900 pc , PSR J0855 - 4644 is a pulsar with one of the highest \dot { E } / d ^ { 2 } from which no GeV \gamma -ray pulsations have been detected . With a dedicated Chandra observation we aim to further resolve the possible jet structures of the nebula and study the pulsar ’ s geometry in order to understand the lack of \gamma -ray pulsations . Methods : We perform detailed spatial modelling to constrain the geometry of the pulsar wind nebula and in particular the pulsar ’ s line of sight ( observer angle ) \zeta _ { PSR } defined as the angle between the direction of the observer and the pulsar spin axis . We also perform geometric radio and \gamma -ray light curve modelling using a hollow-cone radio beam model together with two-pole caustic and outer gap models to further constrain \zeta _ { PSR } and the magnetic obliquity \alpha defined as the angle between the magnetic and spin axes of the pulsar . Results : The Chandra observation reveals that the compact XMM source , thought to be the X-ray pulsar , can be further resolved into a point source surrounded by an elongated axisymmetric nebula with a longitudinal extent of 10 ^ { \prime \prime } . The pulsar flux represents only \sim 1 % of the XMM compact source and its spectrum is well described by a blackbody of temperature kT = 0.2 keV while the surrounding nebula has a much harder spectrum ( \Gamma = 1.1 for a power-law model ) . Assuming the origin of the extended emission is from a double torus yields \zeta _ { PSR } = 32.5 ^ { \circ } \pm 4.3 ^ { \circ } . The detection of thermal X-rays from the pulsar may point to a low value of \lvert \zeta - \alpha \rvert if this emission originates from a heated polar cap . Independent constraints from geometric light curve modelling yield \alpha \lesssim 55 ^ { \circ } and \zeta \lesssim 55 ^ { \circ } , and 10 ^ { \circ } \lesssim| \zeta - \alpha| \lesssim 30 ^ { \circ } . A \chi ^ { 2 } fit to the radio light curve yields a best fit at ( \alpha, \zeta _ { PSR } ) = ( 22 ^ { \circ } , 8 ^ { \circ } ) , with an alternative fit at ( \alpha, \zeta _ { PSR } ) = ( 9 ^ { \circ } , 25 ^ { \circ } ) within 3 \sigma . The lack of non-thermal X-ray emission from the pulsar further supports low values for \alpha and \zeta under the assumption that X-rays and \gamma -rays are generated in the same region of the pulsar magnetosphere . Such a geometry would explain , in the standard caustic pulsar model picture , the radio-loud and \gamma -ray-quiet behaviour of this high \dot { E } / d ^ { 2 } pulsar . Conclusions :