I can't explain why it is incorrect, but its trend higher does not make sense. Perhaps its raising trend or its increasing trend. Even then, it's not very elegant. ... the crime rate in Chicago continued to climb would be better in my estimation.
All I can add to SwissPete's comment, with which I agree totally, is that the problem in your sentence is the misuse of the adjective "higher": (1) it generally is not used after the noun it modifies (we say "higher education" or "higher prices" for example and not "education higher" or "prices higher." (2) when you really mean that something is increasing, you should use increasing or rising. The best idea, probably, is to use "... the crime rate in Chicago continued to climb" as SwissPete suggests. You could also say, "continued to rise."
Thank you all for the insights; particularly Joelline's grammatical take on the subject. I agree that a simpler way of stating the information would have been more clear, but the semi-scientific nature of the writing lent itself to flourishes of unintended verbosity. My guess is that I was subconsciously influenced by too many articles and shows about the stock market; a field which tends to habitually abuse the word "trend."