If you are pursuing your degree in the US or Canada then there is a good chance your institution belongs to the Council of Graduate Schools. Some international schools also belong to this organization.
Many of the best graduate schools in the US/Canada have explicitly endorsed the April 15th Resolution, which states that students should not be obligated to accept a position (or specifically, an offer of financial aid) before April 15th. This is specifically to avoid putting people in the uncomfortable situation you describe, and to maximize the chance of good matches for all students and schools.
I would reccomend this: if the department that sent you the first offer is affiliated with any of the schools listed in the April 15th document, and your acceptance comes with any offer of aid (such as a TA or RA position) then write to the graduate admissions coordinator and ask if they are aware of the resolution and if it would be OK to delay your acceptance until you hear back from the other programs.
If the department that sent you the first offer is not affiliated with any of the schools listed above, then write to the graduate coodinator explaining your situation. Explain that you are hoping to do a PhD in chemistry at a competitive school and it is widespread practice to delay final graduate admissions decisions in that realm until April 15th. Ask if it would be possible to have an extension on the decision, or if it would be possible to accept the offer contingency.