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 ≤ 900 pc, PSR J0855−4644 is a pulsar with one of the highestĖ/d 2 from which no GeV γ-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 γ-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) ζ PSR defined as the angle between the direction of the observer and the pulsar spin axis. We also perform geometric radio and γ-ray light curve modelling using a hollow-cone radio beam model together with two-pole caustic and outer gap models to further constrain ζ PSR and the magnetic obliquity α 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 . The pulsar flux represents only ∼ 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 (Γ = 1.1 for a power-law model). Assuming the origin of the extended emission is from a double torus yields ζ PSR = 32.5 • ± 4.3 • . The detection of thermal X-rays from the pulsar may point to a low value of |ζ − α| if this emission originates from a heated polar cap. Independent constraints from geometric light curve modelling yield α 55 • and ζ 55 • , and 10 • |ζ − α| 30 • . A χ 2 fit to the radio light curve yields a best fit at (α, ζ PSR ) = (22 • , 8 • ), with an alternative fit at (α, ζ PSR ) = (9 • , 25 • ) within 3σ. The lack of non-thermal X-ray emission from the pulsar further supports low values for α and ζ under the assumption that X-rays and γ-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 γ-ray-quiet behaviour of this highĖ/d 2 pulsar.