We have obtained a moderately long (10(5) s) ASCA observation of the Seyfert 1 galaxy Markarian 231, the most luminous of the local ultraluminous infrared galaxy population. In the best-fitting model we do not see the X-ray source directly; the spectrum consists of a scattered power-law component and a reflection component, both of which have been absorbed by a column N-H approximate to 3 x 10(22) cm(-2). About three-quarters of the observed hard X-rays arise from the scattered component, reducing the equivalent width of the iron K alpha line. The implied ratio of 1-10 keV X-ray luminosity to bolometric luminosity, L-X/L-bol similar to 2%, is typical of Seyfert 1 galaxies and radio-quiet QSOs of comparable bolometric luminosities and indicates that the bolometric luminosity is dominated by the active galactic nucleus (AGN). Our estimate of the X-ray luminosity also moves Mrk 231 in line with the correlations found for AGNs with extremely strong Fe II emission. A second source separated by about 2' is also clearly detected and contributes about 25% of the total flux.