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abstract: 'We present the first *Chandra* and *Swift* X-ray study of the spiral galaxy NGC4088 and its ultraluminous X-ray source (ULX N4088–X1). We also report very long baseline interferometry (VLBI) observations at 1.6 and 5 GHz performed quasi-simultaneously with the *Swift* and *Chandra* observations, respectively. Fifteen X-ray sources are detected by *Chandra* within the D25 ellipse of NGC4088, from which we derive the X-ray luminosity function (XLF) of this galaxy. We find the XLF is very similar to those of star-forming galaxies and estimate a star-formation rate of 4.5 $M_{\odot}$ yr$^{-1}$. The *Chandra* detection of the ULX yields its most accurate X-ray position, which is spatially coincident with compact radio emission at 1.6 GHz. The ULX *Chandra* X-ray luminosity, $L_\mathrm{0.2-10.0 keV} = 3.4\ \times$ 10$^{39}$ erg s$^{-1}$, indicates that N4088–X1 could be located at the high-luminosity end of the high-mass X-ray binary (HMXB) population of NGC4088. The estimates of the black hole mass and ratio of radio to X-ray luminosity of N4088–X1 rule out a supermassive black hole nature. The *Swift* X-ray spectrum of N4088–X1 is best described by a thermal Comptonization model and presents a statistically significant high-energy cut-off. We conclude that N4088–X1 is most likely a stellar 