A polymer comprising recurring units of formula (1) is provided wherein some hydrogen atoms of phenolic hydroxyl groups and/or alcoholic hydroxyl groups and/or carboxyl groups are replaced by acid labile groups. The polymer is crosslinked with a crosslinking group having a C-O-C linkage resulting from reaction of some of the remaining alcoholic hydroxyl groups and/or carboxyl groups with an alkenyl ether compound or halogenated alkyl ether compound. The amount of the acid labile group and the crosslinking group combined is on the average from more than 0 mol % to 80 mol % of the entirety of the phenolic hydroxyl group, alcoholic hydroxyl group and carboxyl group. The polymer has Mw of 1,000-500,000. R1 is H or methyl, R2 is C1-C8 alkyl, R3 is a divalent C1-C18 hydrocarbon group which may have a hetero atom, R4 and R5 are H or monovalent C1-C18 hydrocarbon groups which may have a hetero atom, x and y are integers satisfying x+y</=5, x', y' and z' are integers satisfying x'+y'+z'</=5, p, q and r are numbers satisfying 0</=p</=0.4, 0</=q</=0.4, 0.01</=p+q</=0.8, and p+q+r=1. A chemically amplified positive resist composition comprising the polymer as a base resin has high sensitivity, high resolution, a wide latitude of exposure, and process adaptability and forms resist patterns having plasma etching resistance and heat resistance.